A group of men could do a piece of work in 18 days. However, 6 men left the group before the work began and the remaining men in the group completed the work in 20days. What was the original size of the group?
If M1 persons can do a piece of work in D1 days and M2 persons can do same piece of work in D2 days, then M1*D1= M2 * D2.
Let the original number of men in the group be 'x'. (M1)
After 6 men left, the size of group be (x-6) men. (M2)
Now using the above formula, we get
⇒ x * 18 = (x-6) * 20
⇒ 18x = 20x -120
⇒ 120= 20x-18x
⇒ 120 = 2x
⇒ x=60
Therefore, the original number of men in the group is 60 men.
A water tank is 2/5 th full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Since pipe B is faster than pipe A and thus, the tank will be emptied.
Part of the tank to be emptied = 2/5
Part emptied by (A+B) in 1 minute= (1/6 - 1/10) = 1/15.
Therefore,
⇒ 1/15 : 2/5 :: 1: x
⇒ 2/5 * 15 = 6 minutes
A and B together can do a work in 8 days, B and C together in 6 days, while C and A together in 10 days. If they all work together, the work will be completed in how many days?
Formula: A and B together can do a work in x days, B and C together in y days, while C and A together in z days. If they all work together, the work will be completed in: (2xyz)/( xy+yz+zx)
In the above given problem 'x' = 8 days, 'y' = 6 days and 'z' = 10 days.
Substituting the values x, y and z in the formula, If they all work together, the work will be completed in : (2 * 8 * 6 * 10)/((8*6)+(6*10)+(10*8))
⇒ 960/(48+60+80) = 960/188 = 240/47 days
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Governments need to be generous in supporting international humanitarian agencies, whether with food or funds. Stepping-up supply of food to countries worst-hit by the hunger crisis is necessary. While this will help ease the symptoms of the crisis, it will not address its underlying causes. The latter is necessary to address the problem of food insecurity in the world. Humanitarian food aid is important but simultaneously, we need to put in place medium and long-term strategies to address conflict and climate shocks.
Q. Which of the following is the most logical, critical and rational inference that can be drawn from the above passage?
The passage states that humanitarian aid is important but other steps are also required for ending hunger. D appears correct but A is the more logical and critical choice because the passage harps on the importance of medium and long term steps required for addressing hunger which is captured by A. Hence A is the correct answer.
15 men take 20 days to complete a work working 8 hours a day. How many number of hours a day should 20 men take to complete the work in 12 days?
Formula: If M1 persons can do a piece of work in D1 days for h1 hours and M2 persons can do the same piece of work in D2 days for h2 hours,
then: M1D1h1 = M2D2h2.
In the above given problem M1=15 men, D1=20 days, h1=8 hours, M2=20 men, D2= 12 days. Substituting the above values in the formula, we get
⇒ 15 * 20 * 8 = 20 * 12 * h2;
⇒ 2400 = 240 * h2; h2 = 10 hours
Therefore, 10 hrs a day should 20 men take to complete the same work in 12 days.
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
From the given data, we can get
A's one day work = 1/24,
B's one day work = 1/9 and
Cs one day work = 1/12.
Since, B and C start the work and left after 3 days;
the work done by B and C is = 3 *((1/9) +(1/12)) = 7/12.
Therefore, remaining work = 1- 7/12 =5/12.
Time taken by A to complete the remaining work = 24 * 5/12 =10 days.
Aman can complete a piece of work in 5 days, but with the help of his son he can finish the same piece of work in 3 days. Find the time taken by the son alone to complete the work?
If A can do a work in 'x' days and A + B can do the same work in 'y' days, then the number of days required to complete the work if B works alone is given by the formula: ( x * y)/(x-y).
Aman alone takes 5 days (i.e x) to complete a piece of work and along with his son he can complete same of piece of work in 3 days(i.e y).
Therefore, his son alone takes ( x * y)/(x-y) days to complete the same piece of work.
By substituting the given values in formula, his so will take (5 * 3)/(5-3) = 15/2 = 7.5 days.
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
The impact of environmental disasters is immense but unequal. Houses in poorer areas will often be less stable, storm barriers may be weaker, sanitation is often a problem, emergency services will be poorly resourced - and preventing disease outbreaks may be hindered by the poor state of public health services.
Q. Which among the following is the most logical and essential message conveyed by the above passage?
The focus of the passage is on bringing out how disasters unevenly impact the rich and poor. Hence C is the correct answer.
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is opened all the time and B and C are opened one hour each alternatively , the tank will be full in :
Tank filled in one hour when the taps A and B are open = (1/12)+(1/15)= 9/60= 3/20.
Tank filled in one hour when the taps A and C are open = (1/12) + (1/20) = 8/60 = 2/15
Therefore, part of the tank filled in two hours = (3/20) + (2/15) = 17/60.
Part filled in 6 hours = ( 17/60) * 3 = 51/60
Remaining part = 9/60 = 3/20
After 6 hours Now it is (A+B)' s turn
Time taken by the A+B to fill 3/20 part = 1 hour
Therefore, total time taken = 6+1 = 7 hours
If a pipe A can fill a tank 3 times faster than pipe B. If both the pipes can fill the tank in 32 minutes, then the slower pipe alone will be able to fill the tank in?
Let, the time is taken by pipe A = x
Then, time is taken by pipe B = x/3
By substituting these values, we get: 1/x + 3/x = 1/32 x = 128 minutes
A, B and C together earn Rs.300 per day, while A and C together earn Rs.188 and B and C together earn Rs.152. The daily earning of C is?
Daily Earning of A+B+C = Rs 300
Daily Earning of A and C together = A + C = Rs 188 ... (1)
Daily Earning of B and C together = B + C = Rs 152 ... (2)
Adding (1) and (2) we get A+B+2C = 188 + 152 = Rs 340
Therefore, Daily earning of C = 340 - 300 = Rs 40.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs.3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Work done by A in one day = 1/6.
Work done by B in one day = 1/8
Work done by C in one day = 1/3 - (1/6+1/8) = 1/3 -7/24 = (8-7)/24 = 1/24.
A's wage : B's wage : C's wage = 1/6 : 1/8 : 1/24 = 4: 3: 1
Therefore, C's share = (1/8) * 3200 = Rs 400.
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Work done by A in one day = 1/20. o B's 1 day's work (1/12 - 1/20) = (2/60)= 1/30.
B's half day work = (1/30)/2 = 1/60
A and B 's one day work (if B work for half day) = (1/20 + 1/60) = (4/60)= 1/15
Therefore, total number of days to complete the work = 15 days.
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
As the planet warms, we need to be able to predict what populations will be at risk for infectious diseases because prevention is always superior to reaction. The researchers are now working on a map to pin point future changes in the distribution of vector-borne diseases.
Q. Which among the following is the most critical and rational inference that can be drawn from the above passage?
Options B and C are wrong because they are not the key focus of the passage. The passage tells us about the increasing risk of vector borne diseases as a result of climate change and the efforts undertaken by scientists to deal with such threat which doesn't necessarily lead to the inference that the world is ill prepared, even though it might be the case. Hence option A is correct.
A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B on odd days and C on even days?
(A+B)'s 1 day' s work = (1/11 + 1/20 ) = 31/220
(A+C)'s 1 day's work = ( 1/11 + 1/55) = 6/55
Work done in 2 days by them= ( 31/220 + 6/55) = 55/220 = %.
Therefore, Whole work will be done in 8 days
9 kids can finish a bit of work in 360 days. 18 men can finish the same work of piece in 72 days and 12 ladies can finish it in 162 days. In how long can 4 men, 12 ladies and 10 kids together finish the bit of work?
9×360 children = 18×72 men = 12×162 women
⇒ 45 children = 18 men
= 27 women
⇒ 5 children = 2 men = 3 women
Now, 4 men + 12 women + 10 children
= 4 men + 8 men + 4 men
= 16 men
∵ 18 men can complete the work in 72 days.
∴ 16 men can complete the work in =18×72/16 = 81 days
4 men and 6 women complete a piece of work in 8 days while 3 men and 7 women complete it in 10 days. In how many days 10 women can finish the work?
Let 1 man's 1 day work be x and 1 woman's 1 day work be y. then
4x+6 y= 1/8 ••• (1)
3x+7y = 1/10 •••(2)
Multiplying (1) by 3, (2) by 4 and subtracting, we get
10 y = (4/10- 3/8)
= (16-15)/40 = 1/40
⇒ y = 1/400
1 woman's 1 day work = 1/400
10 women's 1 day work = (1/400*10) = 1/40
Hence 10 women can finish the work in 40 days
A works twice as fast as B. If two can together complete a bit of work in 12 days, then B alone can do it in:
Let B's 1 day work =x.
Then , A's 1 day's work=2x
X+2x=1/12
⇒ 3x=1/12
⇒ x=1/36.
B's 1 day work=1/36.
Hence B alone can finish the work in 36 days.
In one minute 3/7 of a tank is filled. How much time will it take to fill the remaining part of the tank?
Part filled in 1 min. = 3/7.
Remaining part = (1- 3/7)= 4/7
Let the required time be x min.
Therefore, 3/7: 4/7:: 1: x
⇒ 3x/7 = (4/7*1)
⇒ x= 4/3 min.
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
The Paris Agreement adopted last year marks the beginning of a new age in climate change response. The global climate pact will have a major impact on public health policy as countries take measures on adaptation and mitigation. Strengthening adaptation is a must in the face of climate change. This includes plans to protect human health from air pollution, heat waves, floods, droughts and the degradation of water resources.
Q. Which of the following option(s) is/are valid statement(s) that support the emphasis on adaptation as suggested in the passage?
1. At present, more than 7 million deaths occur worldwide every year due to air pollution.
2. In 2017, the world had 124 acutely hungry people
3. Epidemics such as cholera, dengue and extreme weather events such as heat waves and floods have increased
Select the correct code from below:
All the three are issues that can be addressed or mitigated by increasing focus on adaptation. Hence all three are correct. Thus, D is the correct answer.
A man travels a distance of 12 km at 3 km/hr, another distance of 12km at 4 km/hr and a third distance of 12km at 6 km/hr. His average speed for the whole journey is:
The Average speed= (Total Distance/Total Time taken)
Time taken to cover first 12 km= (Distance/Speed)= (12/3)= 4 hours
Time taken to cover second 12 km= 12/4= 3 hours
Time taken to cover last 12 km= 12/ 6= 2 hours
Hence, total time taken for whole journey= (4+3+2) hours= 9 hours
Therefore, the average speed of whole journey= (Total distance/total time)
Average speed of man= (36/9)= 4 km/hr
A boat sails 6 km/hr in still water, however it takes thrice as much time in going the same at distance against the current when compared to the direction of the current. Find the speed of the current?
Given condition:
Speed of the boat in still water = 6 km/hr.
Speed of boat in downstream = 3 * speed of boat in upstream.
Let the speed of the current be 'x' km/hr.
Therefore, speed of the boat in upstream (i.e against the current) = (6-x) km/hr.
Speed of the boat in downstream (i.e in the direction of current) = (6+x) km/hr
Now, substituting values in given condition, we get
⇒ (6+x) = 3 * (6-x)
⇒ 6+x = 18-3x
⇒ 4x=12
⇒ x=3 km/hr
Thus, speed of the current = 3 km/hr.
A boat takes 26 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 10 km/hr, what is the distance between A and B?
As per the given information, the velocity of the stream is 4 km/hr.
The speed of the boat in still water is 10 km/hr.
Therefore, speed of boat in downstream = (10+4)= 14km/hr
The speed of boat in upstream = (10-4) = 6 km/hr.
Let the distance between A and B be 'x'. As C is the distance between B and C is x/2.
Total time taken to reach is 26 hours.
Therefore,
x/14 + (x/2)/6 = 26
⇒ x/14 + x/12 = 26
⇒ (7x+6x)/84 = 26
⇒ 13 x /84 = 26
⇒ x/84 = 2
⇒ x = 168.
The distance between A and B is 168 km.
Tina goes to school from her house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If she takes 5 hours in total, then what is the distance between her house and school?
Let the distance between Tina's house and school be 'x' km.
Therefore, time to cover the distance from her house to school = (Distance/ speed) = (x/3) hours.
Similarly, time to cover the distance from her school to house = (x/2) hours.
It is given that total time taken for whole journey= 5 hours.
Thus, (x/3 + x/2)= 5
⇒ ((2x+3x)/6)= 5
⇒ (5x/6) = 5
⇒ 5x=30 or x=6
Thus, distance between her house and school is 6 km
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
The two criteria that an innovator must satisfy are whether the innovation or invention adds to existing technical knowledge and whether it is inventive enough. Patent filings are seen as a measure of the spread of science and technology in a country. Patent protection also provides monopoly rights to the inventor.
Q. Which of the following is the most crucial and logical inference that can be made from the above passage?
Amit can row 8 km/hr in still water. If the river is flowing at 4 km/hr, it takes 1.5 hours to row to a place and back. How far is the place?
It is given that: Speed in still water = 8 km/hr
Speed of the stream = 4 km/hr
Speed of upstream = (8-4) = 4 km/hr
Speed of downstream = (8+4) = 12 km/hr
Total time = 1.5 hrs
Let x is the distance.
Then substituting the values, we get
x/12 + x/4 = 3/2
x = 4.5 km
A train passes two persons walking in opposite directions at a speed of 5 m/s and 10 m/s in 6 seconds and 5 seconds respectively. Find the length of the train?
Let the speed of the train be 's' m/s.
Let the length of the train be 'x' meters.
Relative speed of train and the first person who is moving at the speed of 5 m/s in opposite direction = (s+5) m/s.
Therefore, total distance travelled (i.e length of train) 'x'= Relative speed X time
x = (s+5) * 6 …. ( Eq 1)
Relative speed of train and the second person who is moving at the speed of 10 m/s in opposite direction = (s+10) m/s
Therefore, total distance travelled (i.e length of train) 'x' = Relative speed X time
x = (s+10) * 5 …. (Eq 2)
Since length of the train is same in both the cases, if we equate the equation 1 and equation 2 we get
⇒ (s+5) * 6 = (s+10) * 5
⇒ 6s+30= 5s+50
⇒ 6s - 5s = 50 - 30
⇒ s = 20 m/s (i.e speed of the train)
Now, putting the value of speed of the train in equation 1 (we can put the value equation 2 as well) we get
Length of the train 'x' = (20+5) * 6
x = 25 * 6
x= 150
Therefore, length of the train is 150 meters.
A man covers a distance via auto driving at 70 km/hr and returns back to the beginning point riding on a bike at 55km/hr. What is his average speed for the entire trip?
Average speed = 2xy/(x+y) km/hr
= (2*70*55)/ (70+55) km/hr
= (2*70*55)/125 km/hr
= 308/5 km/hr
= 61.6 km/hr
How much time will a train 171 m long take to cross a bridge 229 m long, if it is running ^at a speed of 45 kmph?
Speed = (45*5/18)m/sec = 25/2 m/sec.
Required time =(171+229)/(25/2) sec.
= (400*2/25)sec. =32 sec.
Read the following passage and answer the item that follow.
Your answer to this item should be based on the passage only.
Agriculture in India needs to become more sustainable even as small and marginal farmers struggle to build resilience against many threats. First, they remain price-takers and economically vulnerable, beholden to traders who set prices, and with limited opportunities to sell at a time of their choice (due to poor storage). Further, decades of intensive agriculture have added to water stress and declining soil health. Farmers rely on groundwater for more than 60% of irrigation needs. Chemical fertilizers, once a boon to boost soil nutrients, have been applied so intensively (particularly urea) that the long-term health of soils is now of deep concern.
Q. Which among the following is the most logical, rational and critical inference that can be made from the above passage?
The passage focuses on bringing out the lack of sustainable practices in Indian agriculture which are creating several issues. All the examples given above are examples of measures undertaken to boost productivity at the expense of sustainability. Hence A is the correct answer.
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is :
Let the speed of two trains be 7x Kmph and 8x kmph (speed of second train)
Then, 8x = 400 kms/4hrs = 100kmph
Therefore, speed of first train = 7x = (8/7) * 100
Speed of first train = 87.5 kmph
A truck covers a distance of 550 meters in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speeds is:
Ratio of speeds = (550 m/60s * 18/5) : (60 * 33/45) = 33: 44 = 3: 4
Reena runs 9 km at a pace of 6 km/hr. At what pace would she have to go amid the following 1.5 hours to have an average speed of 9 km/hr for the whole running session?
Time taken to cover 9 km = 9/6 hrs. = 1.5 hrs
Total time taken = (1.5 +1.5) hrs = 3 hrs.
Total distance covered in 3 hrs = Average speed * Total Time = (9 *3) = 27 km
In 1.5 hrs, distance covered = (27-9) km = 18 km
Required speed = 18/ (3/2) km/hr = (18*2/3) km/hr = 12 km/hr
How long will a boy take to run round a square field of side 35 metres, if he runs at the rate of 9 km/hr ?
Speed = 9km/hr = ( 9 * 5/18)m/sec = 5/2 m/sec
Total Distance = Perimeter of Square
4 * side of the square = 35 *4 = 140 m
Therefore, time taken = Distance /Speed = 140/(5/2) = 140* 2/5 = 28 *2 = 56sec
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Health accessibility and affordability remain a crucial healthcare problem even in the 21st century. Therefore the World Health Organisation chose "Universal Health Coverage" as the theme for World Health Day 2019. India started working towards the universal problem of affordability and accessibility with the introduction of Ayushman Bharat. The scheme gave a family cover of Rs. 5 lac to socio-economically weaker section and roped it many private sector hospitals to deliver the services. Sadly, most of the roped in hospitals are situated in the urban localities and last mile accessibility remains a point of concern in the country with diverse cultures and topography.
Q. Which is the most critical and rational inference that can be made from the above passage?
The passage talks about the goal of universal health coverage and goes ahead and talks about the Ayushman Bharat Scheme which aims to take India closer to universal health coverage. The passage however goes on to mention the issues with Ayushman Bharat which highlight that for the objective of universal health coverage to be attained, we need to iron out the glitches in Ayushman Bharat and hence B is the most accurate option.
Two, trains, one from Mumbai to New Delhi and the other from New Delhi to Mumbai, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. What is the ratio of their speed?
Standard Formula: If two objects A and B begin their journey at the same time from two points P and Q towards each other and after crossing each other they take a and b hours in reaching Q and P respectively, then
A's Speed Vb
B's Speed Va
By looking at the above problem, we can say that, a=9 hours, b=16 hours.
Therefore, Ratio of speeds of two trains = V16/V9 = 4/3 or 4:3
If a train travels at 60 km/hr from Bangalore to Hyderabad and at 80 km/hr on return trip from Hyderabad to Bangalore. What is its average speed for the entire trip?
2xy
Average Speed = km/hr
By looking at the above problem, we can say that, x= 60 km/hr and y= 80km/hr.
Therefore, average speed = [(2 * 60 * 80)/(60+80)] km/hr = 9600/140 = 68. 57 km/hr
Two trains of lengths 150 m and 180 m respectively are running in opposite directions on parallel tracks. If their speed is 50 km/hour and 58 km/hour respectively. In how much time will they cross each other?
Standard Formula: Suppose A and B are two objects with lengths L1 and L2 respectively, and their speeds are S1 and S2 respectively and moving in opposite direction, then
Crossing Time(Ct) = Length of the objects/ Relative speed of the object(s)
Thus, Ct= (L1+L2)/(S1 +S2)
By looking at the above problem, we can say that,
L1 = 150 m,
L2 = 180 m,
S1 = 50 km/hr
S2 = 58 km/hr
Relative speed= (S1+S2)= 108 km/hr or (108 * 5/18) m/s = 30 m/s.
Therefore, crossing time Ct= (L1+L2)/ Relative speed
Ct= (150 m+180 m)/ 30 m/s
Ct= 330 m / 30 m/s = 11 seconds
Amit covers one-fourth of the total distance at 20 kmph, one-fourth at 10 kmph and rest of his journey at 80 kmph. Find Amit's average speed for the whole distance?
Average speed = Total Distance/Total Time
Let the total distance = D Km
Therefore, Time taken to complete first D/4 distance = t1 =(D/4)km/20kmph Time taken to complete second D/4 distance = t2 = (D/4)/10kmph Time taken to complete remaining distance (that is D/2) = t3 = (D/2)/80kmph Therefore, Average speed = Total Distance/Total Time = (D)/(t1+t2+3)
= D/(D/80 + D/40 + D/160)
= D/(2D + 4D + D)/160 = 160 D/7D
Therefore, Average Speed = 22. 85 kmph
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
The history of UN interventions on migration began with the initiation of the International Labour Organization (ILO) in 1919. Even though there have been several conventions and treaties to protect the rights of migrants and refugees over the years, major intervention by international agencies in managing migration occurred during the neo-liberal era, where short-term mobility of labour is important for global capital to thrive. To match the demand for low- and semi-skilled workers, agencies like the World Trade Organization (WTO) and the World Bank promoted business-friendly migration management approaches, while snubbing worker and migrant rights.
Q. Which of the following is the most logical and critical inference that can be drawn from the passage?
A started a business with a capital of 10,000 rupees and four months later B joined him with a capital of Rs 5000. How much A gets more than B in the profit, if the total profit at the end of the year is Rs 2000.
The ratio of the profits will be according to their investment X duration
Ratio of profits of A to B = 10000*12/5000*8
Ratio = 3:1
Total profit = 2000
Hence, profit of A = 1500
Profit of B = 500
Therefore, profit of A is Rs. 1000 more than profit of B.
A zoo consists of only Tigers and Lions. The number of tigers in a zoo is three times the number of lions. Which one of the following numbers cannot represent the total number of animals in the zoo?
Let the number of lions = x
We know that the number of tigers in a zoo is three times the number of lions. Hence, the number of tigers = 3x.
Then, x + 3x = 4x = total number of animals.
Thus the total number of animals is a number that must be divisible by 4.
Here, 42 is the only number which is not divisible by 4.
If Rahul played 25 singles badminton matches and won 17 out of these. If there were no tied or drawn matches, then what is the ratio of the number of matches won by Rahul to the number of matches he lost?
Total matches played = 25
Matches won = 17
Therefore, Matches lost = 25 - 17 = 8
Required Ratio = Matches won : Matches lost = 17 : 8
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio to their ages will become 11:9 respectively. What is Anand's present age in years ?
Then (5x +3)/(4x+3)= 11/9
By solving the equation, we get x=6.
Therefore, Anand's present age= 4x= 24.
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Individuals, groups and leaders who promote human development operate under strong institutional, structural and political constraints that affect policy options. But experience suggests broad principles for shaping an appropriate agenda for human development. One important finding from several decades of human development experience is that focusing exclusively on economic growth is problematic. While we have good knowledge about how to advance health and education, the causes of growth are much less certain and growth is often elusive. Further, an unbalanced emphasis on growth is often associated with negative environmental consequences and adverse distributional effects. The experience of China, with its impressive growth record, reflects these broader concerns and underlines the importance of balanced approaches that emphasize investments in the non¬income aspects of human development.
Q. With reference to the above passage, consider the following statements:
In developing countries, a strong institutional framework is the only requirement for human development and policy options
Human development and economic growth are not always positively inter-related.
Focusing only on human development should be the goal of economic growth
Which of the above statements is/are correct ?
Statement 3 is wrong as the passage states that focussing solely on economic growth is problematic. The corollary of this is not that the focus should only be on human development.
Statement 1 is wrong as there are structural and political constraints as well that need to be taken into account.
Hence D is the most accurate answer.
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters. P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P
⇒ P = 10 liters.
Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?
Vessel A Sugar and Rava ratio = 3 : 2 Vessel B sugar and Rava ratio = 2 : 3
Given,
(2x + 24)/(3x + 16) = 16/19
38x + 456 = 48x + 256
10x= 200
x = 20 litres
Initial quantity = x*5 = 100 litres
In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?
There are two containers P and Q. P contains 56 kg of salt and Q contains 36 kg of sugar. From P 24 kg of salt is taken out and poured into Q. Then 20kg of the mixture from Q is taken out and poured into P. Find the ratio of final quantity of salt to sugar in container P.
initially, the Amount of sugar in Q = 36kg
Now, 24kg of salt is poured in Q,
Total quantity in Q becomes = 36kg (sugar) + 24kg (salt) = 60kg (mixture)
The ratio of salt to sugar in Q becomes = 24 : 36 = 2 : 3
Now, the Amount of salt in P = 56 - 24 = 32 kg
Again, 20kg of the mixture is taken out from Q and poured into P
Therefore, quantity of salt and sugar in P becomes = [32 + 20 * (2/5)] kg of salt + 20 * (3/5) kg of sugar = (32 + 8) kg of salt + 12 kg of sugar = 40 kg of salt + 12 kg of sugar Required ratio = (40/12) = (10/3)
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Many people in India feel that if we cut our defence expenditure on weapon-building, we can create a climate of peace with our neighbours, subsequently reducing the conflict or creating a no-war situation. People who proclaim such ideas are either the victims of war or the propagators of false argument.
Q. With reference to the above passage, which of the following is the most valid assumption?
The underlying assumption in the first part of the passage is captured by B. The passage states that curtailing defence expenditure would reduce the threat of war. Hence B is the correct answer.
A got twice as many marks in English as in Science. His total marks in English, Science and Mathematics is 180. If the ratio of his marks in English and Mathematics is 2 : 3, what is his marks in Science?
English : Mathematics = 2:3
English : Science = 2:1
English : Mathematics : Science = 2:3:1
English + Mathematics + Science = 180
Marks in Science = (1/6)*180 = 30
By mistake, instead of dividing Rs. 117 among A, B and C in the ratio 1/2,1/3,1/4 it was divided in the ratio of 2:3:4. Who gains the most and by how much?
Original ratio of A, B, and C = 1/2 : 1/3 : 1/4 = 6: 4: 3 Share of A = 6/13 * 117 = Rs. 54 Share of B = 4/13 * 117 = Rs. 36 Share of C = 3/13 * 117 = Rs. 27
The ratio of A, B, and C by mistake = 2 : 3 : 4 Share of A = 2/9 *117 = Rs.26 Share of B = 3/9 *117 = Rs.39 Share of C = 13 * 4 = Rs.52
Therefore, it is clear from the above calculation that C gains maximum i.e. 52 - 27 = Rs. 25
The ratio of the number of UG students and PG students in a college is 5:4. If 40% of the UG students and 50 % of the PG students are scholarship holders. What percentage of the students does not get the scholarship?
Let UG students be = 5x and PG students be = 4x respectively
Number of those who do not get scholarship,
= 60% of 5x + 50% of 4x = (60/100*5x) + (50/100*4x)
= 300x/100+ 200x /100 = 3x + 2x = 5x
Required percentage = (5x/9x) *100 = 55.5%
The wages of Santhosh and Revathi are in the ratio ratio 6:5. If the wages of each is increased by Rs.6000, the new ratio becomes 38:35. What is Revathi' s present salary?
Let the original salary of Santhosh and Revathi be 6x and 5x respectively Then, (6x+6000) / (5x+6000) = 38/35 35(6x+6000) = 38(5x +6000)
210x +210000 = 190x + 228000 210x - 190x = 228000 - 210000 20x= 18000 X = 900
Revathi's present salary = 5x = 5*900 = Rs. 4500
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
In 2019, women's actual involvement in politics remains noticeably weak across parties. And nine out of ten of our legislators are men. In the matter of women's actual political representation in Parliament, India ranks 151 globally among 190 countries. Among its eight South Asian neighbours, India ranks below Afghanistan, Bangladesh, Pakistan and Nepal. And (according to the Inter-Parliamentary Forum), as of 2014, India' s women occupied less than 12 per cent seats both in the Lok Sabha and Rajya Sabha. Even in the state and national decision-making bodies, women remain hugely under-represented.
Q. Which of the following is the most logical and rational corollary to the above passage?
The focus of the passage is on highlighting the missing women in Indian politics. The passage seems to suggest that is critical for ensuring equal rights to women.
Hence, A is correct.
The cost price of 2 shirts and 3 jeans is Rs. 2200 and the cost price of 2 jeans and 4 shirts is Rs. 2400. Find the ratio between the cost price of the jeans and the shirt.
Let the cost price of one shirt be x and cost price of one jean be y.
2x + 3y = 2200 ...(i)
2y + 4x = 2400 or 2x + y = 1200 ...(ii)
By solving the equation (i) and (ii),
x = Rs.350; y = Rs. 500
Therefore the required ratio = 500 : 350 = 10 : 7
For every 2 chocolate Mahesh gets Umesh is given 3 chocolate. If the total number of chocolate distributed to them is 65, then find the number of chocolates Umesh received?
Let Mahesh gets 2x chocolates and Umesh gets 3x chocolates.
Total chocolates = 5x =65;
x= 13
Therefore, Total chocolates received by Umesh = 3x = 3 * 13 = 39.
Two numbers are in the ratio 7:9. If 12 is subtracted from each of them, the ratio becomes 3:5. The product of the numbers is:
Given, ratio of two numbers = 7: 9 Let two numbers be 7x and 9x
If 12 is subtracted from each number, then new numbers are (7x -12) and (9x - 12)
It is given that (7x-12)/(9x-12) = 3/5
⇒ 5(7x - 12) = 3(9x - 12)
⇒ 35x - 60 = 27x - 36
⇒ 8x = 24 or x = 3
Product of the numbers = 7x * 9x = 7(3) * 9(3)
= 21 * 27 = 567
Ratio between two numbers is 3:2 and their difference is 25, then find the smaller number ?
Given, the ratio of two numbers = 3 : 2 Let the two numbers be 3x and 2x
Given, their difference = 25
⇒ 3x - 2x = 25
⇒ x = 25
Smaller number = 2x = 2 * 25 = 50
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
School safety' has been defined as the creation of a safe environment for children, starting from their homes to their schools and back. This includes safety from large-scale 'natural' hazards of geological/climatic origin, human-made risks, pandemics, violence as well as more frequent and smaller-scale fires, transportation and other related emergencies and threats that can adversely affect the lives of children. The concept of 'safe school' has evolved over the last couple of decades as the threat to the physical well-being of children has risen both globally and in India. International attention was drawn to the safety of school children in 'The Hyogo Framework for Action: Building the Resilience of Nations and Communities to Disasters', adopted by the United Nations in 2005.
Q. In light of the above passage, which of the following statement(s) is/are true about school safety?
School safety concerns itself with safety of children inside school premises
School safety as an issue has also been raised at disaster management conferences
Select the correct code from below:
School safety includes safety also from school to home. Hence 1 is wrong. School safety has been talked about at Hyogo Conference, Hence 2 is correct. Hence option (b) is correct.
A trader allows two successive discounts of 10% and 20%. If he sells the article for Rs. 144, then what is the marked price of the article?
Always the discount is provided on marked price. Here 2 successive discounts are given.
Let us assume that marked price is M.
So first discount is 10%. Thus the price becomes 9/10th. and the second discount is 20 %. Thus, price becomes 8/10.
After allowing these two discounts price comes out to be 144.
Now representing this mathematically:
M x 9/10 x 8/10 = 144 M x 72/100 =144 M= 144 x 100/72 M= 200
If the length and breadth of a rectangle decrease by 10% each, then by what percent does the area decrease?
Let the length and breadth of the rectangle be x and y units respectively
Original area= xy units2
New area= (0.9x) x (0.9y) =0.81xy units2
Percentage decrease in area= (0 .81xy- xy/xy) x 100= -19% (Negative sign indicates decrease in area)
When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale ?
Let the original price be x and sale be ofy units.
Then, the revenue collected initially = x x y
Now, new price = 0.8 x, new sale = 1.8 y
Then, new revenue collected = 1.44 xy
% increase in revenue = ([0.44xy/xy] x 100) = 44% increase
A shopkeeper sells an article at 12.5% loss. If he sells it for Rs. 92.50 more, then he gains 6%. What is the cost price of the article ?
Selling Price (S.P.) = Rs100 - Rs12.5 = Rs. 87.5
S.P. after 6% gain = Rs106 Difference = Rs.18.5
Therefore, Cost Price (C.P.) = (92.5/18.5) x 100 = Rs.500
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Fortunately, the modern trend in today's world is towards less secrecy and more information. The International Covenant on Civil and Political Rights (ICCPR), adopted by the General Assembly of the United Nations way back in 1966, specifically includes the right to freedom of expression, defined as "the freedom to seek, receive and impart the information and ideas of all kinds".
Q. Which among the following option is in sync with the central theme of the passage?
A milkman sells milk at the rate of Rs 50 per liter. The milk sold contains 25% water. Assuming that the cost of the milk is Rs. 40 per liter, what is the profit per liter made by the milkman?
Milk contains 25% water and 75% milk.
Therefore, 1 liter milk contains only 750 ml of milk.
Cost of 750 ml milk = 40 * (750/1000) = 40 * 3/4 = Rs. 30
Since, 750 ml of milk is diluted to one liter and sold at the rate of Rs. 50 per liter.
Selling price of 1 Liter milk = Rs. 50.
Profit per liter = Rs. 50 - Rs. 30 = Rs. 20.
In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, then what will be the ratio of the number of boys to that of the girls?
Let the number of boys = x
Then, the number of girls (20% more than that of boys) =x+(20/100)x
=(120/100)x
=(6/5)x
Total number of boys and girls in class is 66.
Therefore, x + (6/5)x = 66; x= 30
The number of girls = 66 - 30 = 36
Now, the number of total girls after 4 new girls are admitted to the class = 36 + 4 = 40
New ratio of the number of boys to that of the girls = 30 : 40 = 3 : 4
Ramesh sold an article for Rs. 6,750 after giving a discount of 10% on the labeled price. He would have earned a profit of 50%, had there been no discount. What was the actual percentage of profit earned?
Let the marked price of the article be Rs. x Discount = 10%
Then, the selling price = - 10% of = (9x/10)
Now,= (9x/10)= 6750 Or x = Rs. 7,500
As per the question, if the selling price is Rs. 7,500,
then the profit earned by the Ramesh is 50%.
So, the cost price = Rs. 5,000
Therefore, the actual percentage of profit earned by selling the article for Rs. 6,750 = (Profit/CP) x 100 =(1750/5000)x 100 = 35%
A man buys an article for 20% less than its value and sells it for 20 % more than its value. What is his gain in percentage?
Unconventional Method:
Let's assume actual value of article is Rs. 100.
Therefore, buying price is 100-20 = Rs. 80 (As man bought with 20% less than actual value). Selling price of article is 100 + 20 = Rs. 120 (As man sold with 20% more than actual value). Therefore, gain in percentage = [(120-80)/80] * 100 (40/80) * 100 = 50 %
Hence, option (a) is correct
Formula Method:
Let the original price of the article be 'x'.
Buying price will be (80/100)x = 0.8x.
Selling price will be (120/100)x = 1.2x Therefore, gain in percentage =(profit/buying price) * 100 [(1.2x-0.8x)/0.8 x]* 100 0.5x * 100 = 50 %
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
We have hard work ahead. There is no resting for any of us till we redeem our pledge in full fill we make all the people of India what destiny intends them to be. We are citizens of a great country, on the verge of bold advance, and we have to live up to that high standard. All of us, to whatever religion we may belong, are equally the children of India with, equal rights, privileges and obligations. We cannot encourage communalism or narrow mindedness, for no nation can be great whose people are narrow in thought or action.
Q. The challenge the author of the above passage throws to the public is to achieve
Hard work is a challenge that the author throws to the public in the very first line. The passage also highlights the importance of national unity and not be divided on the lines of religion etc. Hence D is the correct answer.
A and B invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If 'A' invested Rs. 40,000, what is the amount invested by B?
Since profit is divided among A and B is 2:3, their investment also remains in the same ratio 2:3.
Let amount invested by B be x.
Then, 40000/x = 2/3 Or x= 60000
Ramya and Sheela are partners in a business, Ramya invests Rs, 35,000 for 8 months and Sheela invests Rs. 42,000 for 10 months. Out of a profit of Rs. 31,570, What is Ramya's share ?
Since, Ramya invested for 8 months and Sheela invested for 10 months, Ratio of their shares = (35000 * 8 ) : (42000 * 10) = 2 : 3.
Ramya's share Rs. 31570 * (2 / 5) = Rs. 12628.
The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, What is its purchase price?
Purchase price = Rs ( 8748/(1- 10/100)^{3}
= Rs. [8748 * (10/9) * (10/9 )* (10/9)]
= Rs.12000
A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number ?
Let the original number be x.
If number is decreased by 10% and then increased by 10%, then Final number obtained = 110% of (90% of x)
= (110/100 * 90/100 * x)
= (99/100)x.
By the given data, number so obtained is 10 less than the original number,
Therefore x- (99/100)x=10 or x =1000
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Really I think that the poorest he that is in England has a life to live, as the greatest he, and therefore truly, I think it is clear that every man that is to live under a government ought first by his own consent to put himself under the government, and I do think that the poorest man in England is not at all bound in a strict sense to that government that he has not had a voice to put himself under.
Q. The above statement argues for
The passage states that the poor are not bound in a strict sense to the government because of their lack of voice in the government. Hence C is the correct answer.
By selling a pen at a profit of 60% a man got Rs 38 more than one third of its cost price. What is the cost price of pen?
Let the cost price = x
Therefore selling price with 60% profit = 160/100 x =8/5 x
It is given that selling price is 38 more than one-third of cost price
(8/5) * x = x/3 + 38 (8/5 - 1/3) * x = 38 ((24 - 5)/15) * x = 38 x = 38 * 15/19 x = 30
Therefore, cost price = Rs 30
Ramya invested an amount of Rs.60000 to start a business . After 8 months, Bharathi joined her with an amount of Rs .30000. They earned profit Rs. 24500 after one year. What is Bharathi profit ?
Ratio of capital invested by each partner.
i.e Ramya and Bharathi for one year in order to get same profit.
Ramya invested for 12 months whereas Bharathi invested for 4 months. Therefore,
= 12 * 60000 : 4 * 30000 = 720000 : 120000 = 6 : 1
Share of Bharathi out of Rs .24500 = 1/7 * 24500 = Rs. 3500
What is the sum of all natural numbers between 100 and 200 which are multiples of 3?
Multiples of 3 between 100 and 200 are 102, 105, 108, 198.
Here, the first term = 102 last term = 198
Let the number of Multiples of 3 between 100 and 200 = n
Arithmetic Progression Formula: an = a1 + (n - 1)d
Where, an = last term = 198
a1 = first term = 102
d = common difference = 105 - 102 = 3
⇒ 198 = 102 + (n - 1) * 3
⇒ 198 - 102 = (n - 1) * 3
⇒ 96 = (n - 1) * 3
⇒ (n - 1) = 96/3 = 32
⇒ n = 32 + 1
⇒ n = 33
Formula: Sum of n terms = Sn = (n/2) * (a1 + an )
where n = number of elements = 33
a1 = first term = 102
an= last term = 198
Thus, using the above formula, Sum of all natural numbers between 100 and 200 which are multiples of 3 = (33/2) * (102 + 198)
= (33/2) * 300
= 33 * 150
= 4950
One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
Let the given number be : x
It is given that x/2 - x/3 = 6
Or x/6 =6 or x =36
Therefore, sum of the digits 3+6 = 9
Directions for the following (one) item:
Read the following passage and answer the item that follow. Your answer to this item should be based on the passage only.
Automation will likely impact most jobs involving highly structured physical activity in predictable environments, such as manufacturing and retail, alongside data collection and processing. Also, automation threatens to impact women more than men, suggests the report. It points out that women are a large component of the workforce in retail, business processing outsourcing and textiles/clothing /footwear.
Q. Which of the following is the most logical and crucial inference that can be drawn from the passage?
The most crucial and critical inference that can be drawn from the passage is A as the passage does give example of jobs involving routine work which are more at threat due to automation. Hence A is the correct answer.
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