OPSC OAS Prelims Paper 2 Mock Test - 4 - OPSC OCS (Odisha) MCQ

• 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.

• 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

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.

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.

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.

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.

The focus of the passage is on bringing out how disasters unevenly impact the rich and poor. Hence C is the correct answer.

• 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

Daily Earning of A+B+C = Rs 300

1. Daily Earning of A and C together = A + C = Rs 188 ... (1)

2. 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.

• 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.

• 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.

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)'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

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.

• 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.

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.

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

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.

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

Correct answer- option C

a) Most inventions are too trivial to qualify for patent protection.

• Incorrect: The passage does not indicate that most inventions are trivial; it merely outlines criteria for what qualifies as patentable.

b) Patent filings are often irrelevant to the actual technological advancements made.

• Incorrect: This option contradicts the passage, which states that patent filings are a measure of the spread of science and technology.

c) Patent protection incentivizes innovation and is essential for technological progress.

• Correct Answer: This option directly aligns with the passage, as it highlights the importance of patent protection in fostering innovation and technological growth.

d) Patent protection is only beneficial for large corporations, not individual inventors.

• Incorrect: The passage does not limit the benefits of patent protection to large corporations, thus making this option misleading.

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.

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.

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

• Ratio of speeds = (550 m/60s * 18/5) : (60 * 33/45) = 33: 44 = 3: 4

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.

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

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

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

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.