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Walking at 6/7^{th} of his usual speed, a man is 12 minutes late. The usual time taken by him to cover that distance is
S_{1}: S_{2} = 6 : 7
1 T :T 2 = 7 : 6 (S ⍺ 1 / T)
Difference between
T_{1} & T_{2} = 1 (7  6 = 1)
If 1 = 12min.
then 6 = 72 min. = 1 hrs 12min.
In selling an article for ₹ 76, there is a profit of 52%, if it is sold for ₹ 75, then the profit percent will be.
152% = 76
100% = Cost price = 76 / 152 x 100
C.P = Rs. 50
New selling price = 75
% profit = 75  50 / 50 x 100%
= 25 / 50 x 100% = 50%
The lines x + 3y = 4 and 3x – y = 6 intersect the y – axis at A and B respectively. AB = ?
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
Approximately what is the average number of items sold for all the years together?
≃ 63 lakh(Appx.)
Area of a circle is equal to the area of a rectangle having a perimeter of 100 cm and length is more than the breadth by 6 cm. What is the diameter of the circle?
Let breadth = x, then length
= (x + 6)
2(x + x + 6) = 100
2x + 6 = 50
x = 22 cm
Breadth = x = 22 cm & length
= 22 + 6 = 28 cm
Area of circle = Area of rectangle ir
⇒ r^{2} = 22 x 28
⇒ r^{2} = 22 x 28 / 22 x 7 = 7 x 4 x 7
⇒ 7 x 2 = 14 cm
So, Diameter = 2r = 28 cm
Seema purchased an item for Rs.9,600 and sold it for a loss of 5 percent. From that money, she purchased another item and sold it for a gain of 5 percent. What is her overall gain/ loss?
SP = 9600 x 95 / 100 = Rs. 9,120
Second S.P. = 9120 x 105 / 100 = Rs. 9,576
Loss = 9600  9576 = 24
A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make water 20% in the new mixture?
Milk =90/100 × 40 = 36 litres
water = 5 litres
5x + 20 = 40 + x
X = 5
The average weight of 8 persons increases by 2.5 kg when one person whose weight is 65 kg is replaced by a new person. What Is the weight of the new person?
Weight of new person = 65 + 20 = 85 kg
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
During which year the percentage of items unsold was the highest?
% in 2002 = {(10 x 100) / 70}% = 14.3%;
% in 2003 = {(10 x 100) / 65}% = 15.38%;
% in 2004 = {(15 x 100) / 80}% = 18.75%;
% in 2005 = {(10 x 100) / 60}% = 16.67%;
% in 2006 = {(15 x 100) / 75}% = 20%;
% in 2007 = {(10 x 100) / 90}% = 11.11%;
and % in 2008 = {(5 x 100) / 70}% = 6.25%;
It was the highest in 2006.
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
Approximately what is the average number of items unsold for all the years together?
Average = (10+10+15+10+15+10+5)/7 = 75/7 lakh
≈ 1,07,000 lakh(Aprx)
A, B and C can finish a work in 8 days, 10 days and 12 days respectively. They worked together and get Rs. 740. How much will each of them will get?
Given,
1 day work of A, B & C is 1 / 8, 1 / 10, 1 / 12 respectively
therefore , Their shares in money = 1/8 : 1/10 : 1/12 = 15 :12 : 10
Sum of their share = ₹740 x 15/37 = ₹300
B’s share = ₹740 x 12/37 = ₹240
C’s share = ₹740 x 10/37 = ₹200
A room 8 m long, 6 m broad and 3 m height has two windows 1 1⁄2 m × 1 m and a door 2 m × 1 1⁄2 m. Find the cost of papering the walls with paper 50 cm wide at 25 paise per meter.
Area of walls = 2(Length + Breadth) x height
= 2(8 + 6) x 3 = 84m^{2}
Area of two windows and a door = (1 ½ x 1) + 2 x 1 ½ ) = 6m^{2}
Area to be covered = 84  6
= 78m^{2}
Area of paper = Area to be covered = 78
⇒ (length x breadth) of paper is 78
⇒ length of paper = 78/50 x 100m
= 156 m
So, Cost = 156x25 / 100 = Rs.39
Two circles with radii R and r touch each other externally. A direct common tangent with length l is drawn to the circles. Which is true?
Length of direct common tangent l^{2 }= d^{2} – (R – r)^{2}
Here, d = R + r
Therefore, l^{2} = (R + r)^{2} – (R – r)^{2} = 4Rr
= 2√Rr
A certain sum, invested at 4% per annum at compound interest, compounded halfyearly, amounts to Rs. 7,803 at the end of one year. Find the sum.
If interest is compounded halfyearly rate will be 2 %
C.I. for 2 years = 4.04%
Principal = 7803 / 104.04 x 100
= Rs.7500
Read the following bar graph which represents a company's manufacturing and selling(in lakh) of product from 2002 to 2008 and answer the following questions.
The number of items manufactured in 2007 is what percent of the total number of items manufactured in all the years together? (Rounded off to two digits after decimal)?
Reqd. % = {(90 x 100) / 520}% = 17.307% = 17.31 % (Appx.)
Find the measures of an angle that is the complement of 50°.
Let the measure of angle = x°
measure of its complement = 50°
∴ x° + 50°= 90° ⇒ x° = 40°
If sin (10° 6’ 32" ) = a, then the value of cos (79° 53’ 28”) + tan (10° 6’ 32”) is:
cos 79^{o} 53’ 25” + tan 10^{o} 6’ 32”
= sin 10^{o }6’ 32” + sin 10o 6’ 32” / cos 10^{o }6’ 32”
If cos T = 3/5 and if sin R = 8/17, where T is in the fourth quadrant and R is in the second quadrant, then cos (TR) is equal to:
We have
cos T = 3/5
sin T =
=
= √16/25 = ⅘ (Since T is in IV quadrant)
sin R = 8 /17
cos R =
=
√225 / 289 = 15/17 (Since r is in II quadrant)
Now, cos (TR) = cos T cos R + sin T sinR
=
=
= 77/85
There are 13 white and 7 black balls in a bag. Two balls are drawn at random. What is the probability that they are of the same colour?
The ratio between the angles of a quadrilateral is 3:4:6:7. Half of the smallest angle of a quadrilateral is the angle of a cyclic quadrilateral. Find another angle of the cyclic quadrilateral?
Let smallest angle is 3x
So,
3x + 4x + 6x + 7x = 360°
Smallest angle = 54°
According to given condition one angle of Cyclic quadrilateral = 27°
Another = 180 – 27 = 153°
A, B and C divide an amount of Rs. 9,915 amongst themselves in the ratio 3:5:7 respectively. What is the C’s share in the amount?
A : B : C
3 : 5 : 7
Sum of their ratio = 3 + 5 + 7
= 15 units
Share of C = 7/15 × 9915 = 4,627
60 boys working 7 hours a day can do work in 18 days. In how many days will 28 boys working 9 hours a day do the same work?
Using the formula M_{1}D_{1}H_{1}W_{2} = M_{2}D_{2}H_{2}W_{1}
Since work is same for the two cases
M_{1}D_{1}H_{1} = M_{2}D_{2}H_{2}
⇒ D_{2} = M1D1H1 / M_{2}H_{2} = 60 x 7 x 18 / 28 x 9
= 30 days
What should come in place of the question mark (?)?
(833.25 – 384.45) ÷ 24 = ?
(d) ?= (833.25–384.45)/24 = 448.8/24 = 18.7
The average of three numbers is 135. The largest number is 195 and the difference between the other two is 20. The smallest number is:
According to the question,
195 + x + x + 20 = 135 x 3
⇒ 2x + 215 = 405
⇒ 2x = 405  215 = 190
∴ x = 190 / 2
= 95
= smallest number
Distance between the parallel lines 3x + 4y – 15 = 0 and 9x + 12y – 20 = 0 is
3x + 4y  15 = 0
Or 9x + 12y 45 = 0………………..(1)
And 9x + 12y  20 = 0………………(2)
The distance between two parallel lines
ax + by +c_{1} = 0 and ax + by +c_{2} = 0 is
=
= 25/15 = 5/3 units
In a container of 56 litres the ratio of petrol to oil is 6:1. How much oil must be added to the mixture to make this ratio 2:1?
Quantity of petrol = (6/7) x 56 = 48 Litre
Quantity of oil = (1/7) x 56 = 8 litre
Given, New Ratio = 48/8+x=12
48 = 16 + 2x
2x = 48 – 16
2x = 32
x = 16
16 litre is to be added
'A' starts a business with ₹ 3,500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3 what is B's contribution to the capital?
Let B’s investment be Rs x then
3500 x 12/x X 7 = ⅔
⇒ 6000 x 3 = 2x
⇒ x = ₹9,000
If a = 12, b = 13 and c = 14, then the value of b² c² + c² a² + a² b² – a⁴ – b⁴ – c⁴ is.
b² c² + c² a² + a² b² – a⁴ – b⁴ – c⁴
= −12(2a⁴ + 2b⁴ + 2c⁴ – 2a² b² – 2b² c² – 2c² a²)
= −12[(a² − b²)² + (b² – c²)² + (c² – a²)²]
= −12[(144 − 169)² + (169 – 196)² + (196 – 144)²]
= −12[( −25)² + (27)² + (52)²] = –2029
The midpoint of the line segment joining (3,8) and (x + 2, 2) is (4, 5). What is the value of X?
Midpoint of (x_{1}, y_{1}) and (x_{2}, y_{2})
X = (x_{1} + x_{2})/2
4 = (3 + x + 2)/2
⇒ (x+5)/2 = 4 ⇒ x = 3
A man saves 25% of his salary. If due to price rise he increases his monthly expenses by 25% and he is able to save only Rs. 25 per month. Find his monthly salary.
Expenses before price rise = 100  25 = 75
25% increase in expenses = 100 + 25
= Rs. 125
Monthly Expenses = (75 x 125) / 100
= 375/4
Saving = 100  375/4 = 25/4
If saving in 25/4 then salary = 100
IF saving in 25 then salary
= (100 x 25 x 4)/25
= Rs. 400
In the following questions below are given some statements followed by some given conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Give answer:
Statements:
Some pens are blue.
Some pencils are pens.
Conclusions:
I. Some pens are green.
II. Pencil is blue.
(OR)
None of the two conclusions follows.
Choose the alternative which closely resembles the mirror image of the given figure.
In these questions, statements are given followed by two conclusions I and II. You have to consider both the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions is/are definitely drawn from the given statements. Select answer as (a) If only I follows (b) If only II follows (c) If neither I nor II follows (d) If both I and II follow
Statements:
A. All tables are books.
B. All pens are books
Conclusions:
I. All tables are pens.
II. All pens are tables.
Which of the following expressions will be true if the given equation 5x  8 < 12 is definitely true ?
5x  8 + 8 < 12 + 8
5x < 20
x < 4
If DEAR is written as EDFEBASR, then MUST can be written as:
Therefore, MUST can be written as NMVUTSUT
In these questions, statements are given followed by two conclusions I and II. You have to consider both the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions is/are definitely drawn from the given statements. Select answer as (a) If only I follows (b) If only II follows (c) If neither I nor II follows (d) If both I and II follow
Statements:
A. Most lilies are roses.
B. Some roses are daffodils.
Conclusions:
I. Some daffodils are roses.
II. Some lilies are daffodils.
Five bells commence tolling together and toll at intervals of 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
L.C.M. of 4, 6, 8, 10, and 12 is 120.
So, the bells will toll together after every 120 seconds (2 minutes).
In 30 minutes, they will toll together 30/2 + 1 = 16 times.
In a certain code language RECTORY is written as UMUSHAN. How will VIADUCT be written in that code language?
Similarly,
Seats for Science, Arts and Commerce in a school are in the ratio 6:9: 10. There is a proposal to increase these seats by 30%, 20% and 65% respectively. What will be the ratio of increased seats?
Number of increased seats are (130% of 6x), (120% of 9x) and (165% of 10x).
(130/100×6x) : (120/100 × 9x) : (165/100 × 10x)
= 78x : 108x : 165x
= 26 : 36 : 55
How many meaningful English words can be made with the letters ‘P E A R’ using each letter only once in each word?
Given below is a statement followed by 2/3 Assumptions. An assumption is something not written directly but can be considered as the implicit understanding before writing any text, document or writing. Choose the implicit assumption in the following question:
Statement: TATA passenger bus manufacturing company announced a sharp reduction in the prices of their luxury Buses.
Assumptions:
I. There may be an increase in the sale of their luxury buses.
II. The other such bus manufacturers will also reduce their prices.
In these questions, statements are given followed by two conclusions I and II. You have to consider both the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions is/are definitely drawn from the given statements. Select answer as (a) If only I follows (b) If only II follows (c) If neither I nor II follows (d) If both I and II follow
Statements :
All goats are wolves.
Some wolves are tigers.
Conclusions :
I. Some goats are tigers.
II. Some tigers which are wolves are not goats.
Neither I nor II follow.
How many such pairs of letters are there in the word ESTABLISHMENT each of which has as many letters between them in the word as in the English alphabet?
In each of the following questions, select the related word/letters/number from the given alternatives.
Clock : Time : : Calorimeter : ?
In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find out which of the statements is/are sufficient to answer the given question. Choose the correct alternative for each question.
Find Ratnesh's present age, if
I. Five years ago, Ratnesh's age was double that of his daughter's age at that time.
II. Present ages of Ratnesh and his daughter are in the ratio of 11:6 respectively.
III. Five years hence, the respective ratio of Ratnesh's age and his daughter's age will become 12:7.
1) Present ages of Ratnesh and his daughter will be 11x and 6x years respectively.
2) 5 years ago, Ratnesh's age = 2 x His daughter's age
3) 5 years hence, Ratnesh's age/daughter's age = 12/7
Clearly, any two of the above will give Ratnesh's present age Therefore, the correct answer is (d).
Question: In which year was Neha born?
Statement I: Neha at present is 20 years younger to her mother.
Statement II.: Neha"s brother, who was born in 1970, is 25 years younger to his mother.
Age of mother be = x
Age of Neha = x 20
Age of Neha's brother = x+25
Difference between the age of Neha and Neha's brother = x20x+25
= 5 years
Thus, Neha is 5 years younger to her brother
Therefore, Neha was born in 1965.
So both statements I and II are required.
Which answer figure will complete the pattern in the question figure?
In this question, choose the correct water image of the figure (X) from amongst the 4 alternatives.
Read the following information carefully and answer the question given below
Eight persons F, G, H, I, J, K, L and M all are sitting around a rectangular table facing the centre. In which four are sitting on the corner and four are middle at the line. All are like different colour Red, Blue, Brown, Yellow, Green, Grey, pink and purple. (Not necessary in the same order).
F is sitting third to the right of I and third to the left of K. The person who likes red colour is the neighbour of J. The person who likes grey colour is sitting second to the right of F and second to the left of L. Green is the neighbour of grey. K likes pink colour. Blue and brown colour are not the neighbours of purple and pink. F likes purple colour. I like the colour blue. G does not like green, grey and brown colour. M does not like the green colour. M sits at the corner.
Which of the following colours is liked by M?
Read the following information carefully and answer the question given below
Eight people F, G, H, I, J, K, L and M all are sitting around a rectangular table facing the centre. In which four are sitting on the corner and four are middle at the line. All are like different colours: Red, Blue, Brown, Yellow, Green, Grey, pink and purple. (Not necessary in the same order).
F is sitting third to the right of I and third to the left of K. The person who likes red colour is the neighbour of J. The person who likes grey colour is sitting second to the right of F and second to the left of L. Green is the neighbour of grey. K likes pink. Blue and brown colour are not the neighbours of purple and pink. F likes purple colour. I like the colour blue. G does not like green, grey and brown colours. M does not like the green colour. M sits at the corner.
Which of the following options denoted the group of persons sitting at the corner of the rectangular table?
In the question, a piece of paper is folded and cut as shown below in the questions figures. From the given option figure, indicates how it will appear when opened.
In a family of Six members, A, B, C, D, E and F. A and B are married, A is a male member. D is the son of C, who is the brother of A. E is the sister of D. B is the daughterinlaw of F, whose husband has died.
How is C related to B?
C is the brotherinlaw of B.
In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements are sufficient to answer the question. Read all the statements carefully and find out which of the statements is/are sufficient to answer the given question. Choose the correct alternative for each question.
How is Monika related to Praveen?
Statement I: Ramesh is the father of Praveen and Monika is the Granddaughter of Sima.
Statement II: Ramesh is only one son of Sima
Statement I and II together required to answer the question
The term 'Skeet' is associated with which of the following sports/games?
Skeet shooting is a recreational and competitive activity where participants, using shotguns, attempt to break clay targets mechanically flung into the air from two fixed stations at high speed from a variety of angles.
Match the following countries with their respective continents.
A. Tunisia  1. Africa 
B. Hungary  2. South Africa 
C. Vietnam  3. Europe 
D. Chile  4. Asia 
A. Tunisia  Africa 
B. Hungary  Europe 
C. Vietnam  Asia 
D. Chile  South Africa 
Who invented the 'Crescograph' in the 20th Century?
It is a device for measuring plant growth.
Where was the 12th World Congress on Mountain Medicine organised recently?
The theme of the 4day congress was "Mountain Medicine in the Heart of the Himalayas".
The event focused on the science and research aspects of highaltitude medicine for the advancement of human healthcare.
Who was recently appointed as the new Chief Election Commissioner of India?
He succeeded Om Prakash Rawat.
He is a former bureaucrat with the government of India.
Which of the following Public Sector Undertaking was recently conferred with the status of 'Miniratna'?
NPCC incorporated in 1957.
Fields Medal is a prestigious award given for which of the following categories?
• The prize was inaugurated at the request of Canadian mathematician John Charles Fields, who ran the 1924 Mathematics Congress in Toronto.
• Each winner receives a 15,000 Canadiandollar cash prize.
• At least two, and preferably four people, are always honoured in the award ceremony.
Who among the following demonstrated authoritatively that white light is composed of the different colours of the spectrum?
Through his experiments with prisms, he was the first to authoritatively demonstrate that white light is composed of the different colours of the spectrum.
Seven colours constitute white light: red, orange, yellow, green, blue, indigo, and violet.
ADB & Central Government signed a $200 million loan to finance widening and upgrading of about 230 Kilometres State Highways in which state?
Smriti Irani  Textile Ministry 
Rajyavardhan Singh Rathore  Ministry of Youth Affairs and Sports 
Alphonse K  Ministry of Tourism 
Ram Vilas Paswan  Ministry of Consumer Affairs, Food and Public Distribution 
'Hausla 2018', an interChild Care Institution festival was recently organised in New Delhi by which of the following ministries?
"Child Safety" was the theme for 2018.
It provided a platform for the children from CCIs to showcase their talent in their respective domains.
Which of the following organisations publishes 'Gender Inequality Index'?
The United Nations Development Programme (UNDP) is the United Nations' global development network.
Headquarters: New York City, USA
Unnakoti is an ancient site with exotic sculptors of great precision idols carved out of rocks situated in which of the following states?
Unakoti translates to "less than a crore in number" and has several discovered and yettobediscovered sculptures of Hindu gods and goddesses.
A giant 30ftlong carving of Lord Shiva's head called Unakotishwara Kal Bhairav is revered most of all.
Which of the following is India's largest Container Port?
It is a major Port that recently through various initiatives implemented Ease of Doing Business to create value for trade and achieved significant improvements in Port performance metrics.
Which of the following won the Davis Cup 2018 title?
The 2018 Davis Cup is the 107th edition of the Davis Cup, a tournament between national teams in men's tennis.
Croatia won the Davis cup title 13 years after its first title.
If the gravitational acceleration at any place is doubled, then the weight of the body will be
If at high altitudes, birds become rare, the plants likely to disappear are
If at high altitudes, birds become rare, the plants likely to disappear are Rhododendron
Which of the following is a nonmetal that remains liquid at room temperature?
A body moving in a circular path with constant speed has
If we throw a Stone with some speed in a horizontal direction it follows a ……………. path as it falls to the ground.
Which of the following has a maximum metallic character?
Wrought Iron is the purest form of Iron. It contains 0.12–0.25 carbon.
Molecular mass of H_{2}SO_{3} sum of individual atomic masses
= 2 x 1 + 1 x 32 + 3 x 16 = 82
In wind power, which form of energy is converted into electrical energy?
Which instrument is used for measuring relative humidity?
Which one of the following has maximum genetic diversity in India
What is the key ingredient of Vinegar that you use in your diet?
Which of the following roofs provide better protection against fire?
What principle/law explains the working of the hydraulic brakes in automobiles?
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