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IBPS 2017 Examinations: Quants --  DIFFICULTY LEVEL 3

1. A tank is filled with water through five pipes. The first pipe can fill it in 40 minutes; the second, the third and the fourth together can fill it in 10 minutes; the second, the third and the fifth fill it in 20 minutes; the fourth and the fifth together in 30 minutes. In what time will the tank be filled if all the five pipes work simultaneously?
a)  minutes   b)  minutes   c)  minutes   d)  minutes   e) None of these
2. A 100 m long train passes a man, running in the same direction at 6 km/hr, in 5 second and a car travelling in the same direction in 6 s. At what speed is the car travelling (length of both the man and car is negligible)?
a) 18 km/hr   b) 20 km/hr   c) 24 km/hr   d) 30 km/hr   e) None of these
3. In a race of 200 m A beats S by 20m and N by 40m. If S and N are running a race of 100m with exactly the same speed as before, then by how many metres will S beat N?
a) 11.11m   b) 10m   c) 12m   d) 25m   e) None of these
4. There are 3 contains A, B and C which contain water, milk and acid respectively in equal quantities. 10% of the content of A is taken out and poured into B. Then, the same 10% from B is transferred to C, from which again the same 10% is transferred to A. What is the proportion of milk in container A at the end of the process?
a) 9/10   b) 1/11   c) 1/121   d) 10/1011   e) None of these
5. A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 45 extra white balls, making the ratio of white balls to yellow balls . How many white tennis balls did the store originally order for?
a) 450   b) 270   c) 225   d) 230   e) None of these
6. Sumit works as a state contractor for PWD and supplies bitumen mix for road construction. He has two varieties of bitumen, one at Rs. 42 per kg and the other at Rs. 25 per kg. How many kg of first variety must Sumit mix with 25 kg of second variety, so that he may, on selling the mixture at Rs. 40 per kg, gain 25% on the outlay?
a) 30   b) 20   c) 25   d) 15   e) None of these
7. A shop stores  kg of rice. The first customer buys half of this amount plus half a kg of rice. The second customer buys half of the remaining amount plus half a kg of rice. Then, the third customer also buys half of the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
a)    b)    c)    d)     e) None of these
8. What is the area of the face of a clock described by its minute hand between 9 a.m. and 9.35 a.m., if the minute hand is 10 cm long?
a)    b)    c)    d)    e) None of these
9. If the numerator and the denominator of a fraction are each increased by 4, the fraction becomes  and when numerator and denominator of the same fraction are each decreased by 6, the fraction becomes . The sum of the numerator and the denominator is :
a) 11   b) -11   c) 25   d) -25   e) None of these
10. To open a lock, a key is taken out of a collection of n keys at random. If the lock is not opened with this key, it is put back into the collection and another key is tried. The process is repeated again and again. It is given that with only one key in the collection, the lock can be opened. The probability that the lock will open in n trials is :
a)    b)    c) 1-    d) 1-    e) None of these
11. A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
a) 24   b) 18   c) 32   d) 27   e) None of these
12. In a local election, 2400 people were to vote for Party A or Party B. Party A was bound to win the election. However, on Election Day, 33.33% of the voters of Party A were kidnapped. Party B was also able to influence the remaining Party A voters and thus double the strength of its voters. In this way, Party A lost by a majority which was half of that by which it would have won had the elections been fair. How many people finally voted for Party A and Party B?
a) 600(A), 1200(B)   b) 300(A), 600(B)   c) 450(A), 900(B)   d) 600(A), 900(B)
(e) None of these
13. Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?
a) 60 kmph   b) 80 kmph   c) 20 kmph   d) 40 kmph   e) None of these
14. A trader marked his goods at 20% above the cost price of Rs. 245346. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is,
a) 2%   b) 15%   c) 2.75%   d) 13.5%   e) None of these
15. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
a) 2160   b) 3120   c) 3972   d) 6240   e) None of these
SOLUTION
1. c)
 Pipes Time Efficiencies (unit/min), if total capacity of tank = 120 unit P1 40 min 3 P2+P3+P4 10 min 12 P2+P3+P5 20 min 6 P4+P5 30 min 4
Efficiency of (P2 + P3 + P4 + P5) =
Efficiency of (P1 + P2 + P3 + P4 + P5) = 3 + 11 = 14
Time required to fill the tank =
2. a) Let speed of train = x kmph and speed of car =  y kmph then according to question
x = 78 kmph
Again,                       60 = 78 – y            y = 18 kmph
3. a) In the time that a takes to run 200nm S runs 180m and N. runs 160m
So in the time that S takes to run 200m, N runs = 200
Or ‘N’ is beaten by 22.22 m
In 100 metre race N is beaten by 11.11m
4. d) Let amount of water, milk and acid in containers A, B and C respectively = 100x
Water remaining after 10% content of A taken out = 90x(water)
Now milk and water in ‘B’ = 100x (milk) and 10x (water) 10% content of B = 10x (milk) and x(water)
After pouring 100% content of B into ‘C’ the content of C = 100x (Acid), 10x (Milk) and x(water)
10% content of ‘C’ induces = 10x (acid), x (milk) and (water)
Now after pouring 10% content of ‘C’ into A, the content of A =  (water), x(milk) and 10x(acid)
Proportion of milk in container ‘A’ =
5. c) Ratio of white to yellow balls = 6:5
Let white balls = 6x
And Yellow balls = 5x
Now, 6x – 5x = 45                  x = 45
Available white balls = 6 x 45 = 270
Ordered white ball = 270 – 45 = 225
6. e) Let x kg of first variety is mixed with second variety required cost price =
Now apply allegation

32

7                      10
Now x =                        x = 17.5 kg
7. b) Quantity of rice left after the first transaction = x -
Quantity of rice left after second transaction =
Quantity of rice left after third transaction =
And it is given that =          x = 7
8. b) Total angle rotated by clock in 35 minute = 35 x 6 = 210 Now area =
=
9. c) Let numerator of fraction = x and denominator Now according to question
x – 2y = 4        …(i)
And again,                 x – 12y = -66   …..(ii)
Solve equation (i) and (ii)
We get x = 18, y = 7     x + y = 25
10. c) Probability that the lock is opened in a trial =
( only one key, which opens the lock)
the chance that the lock is not opened in a particular trial = 1 -
Probability (lock is opened in n trials) = 1 – p (lock is not opened in ‘n’ trials)
= 1 –
11. d) et ‘n’ good required to sell for making 40% profit
Total ‘CP’ = 20n         Total ‘SP’ =
56 = 4 + 2n – 2            2n = 54            n = 27
12. a) Let party A’s voter before kidnapping and influence = x
After kidnapping voter of panty A =
Party B’s voter = 2400 – x
After influence B’s voter = 2(2400 – x)
Then A’s voter =                 Now according to question,

=                            x = 1800
Vote given to party A =
Vote given to party B =
13. a) Let speed of first car, second car and third car are x, y, and z km/hr respectively.
Now according to question,                     (Where ‘d’ is distance between A and B)
…..(i)            Now again,                            …(ii)
Further,
From equation we can get ‘y’ in terms of x and z                  x : y : z = 1 :  : 2     or,
x : y : z = 3 : 4 : 6        and    is give      1 20
Difference between speed of first and third car = (6-3) = 3
Required difference = 3 x 20 = 60 kmpr
14. a) Profit on half of the stock = 20%   Loss of another  of stock = 4%
Apply allegation,

(?)                    Profit on  stock

20 - ? = 8         ? = +12% (profit)
Loss on another  stock = 20 – 40 -
Use again allegation

(?)                    overall profit

12 - ? = 10       Or, ? = 2%
15. c) Increase in amount in 6 years = 60%
Hence rate = 10% per annum
Compound interest =          =