IBPS PO MAINS 2016 - Quant Quiz-13 (Mixed)

1. A vessel is full of a mixture of petrol and kerosene in the ratio 7 : 5. 9 litres of this mixture is taken out and replaced with kerosene. The ratio of petrol to kerosene in the vessel is now 7 : 9. What is the volume of the vessel ?

A. 24 ltrs
B. 36 ltrs
C. 18 ltrs
D. 28 ltrs
E. None of these

Sol. Suppose the quantities of petrol and kerosene in the vessel are 7x and 5x respectively.
The 9 litres of this mixture that is taken out will contain petrol and kerosene in the ratio 7:5.
So, the quantity of petrol removed is (7/12) × 9 = 5.25
And the quantity of kerosene removed is (5/12) × 9 = 3.75.
Then 9 litres of kerosene is added to the mixture.
The quantity of petrol is now (7x – 5.25)
And the quantity of kerosene is (5x – 3.75 + 9) = (5x + 5.25).
From the given information, (7x – 5.25) / (5x + 5.25) = 7/9.
Solving this equation yields x = 3. Thus the volume of the vessel is 7x + 5x = 12x = 36 litres.

2. A sum of Rs 500 was divided among 50 boys and girls. Each boy gets Rs 12 and a girl gets Rs 8. Find the no. of boys and girls ?

A. 25, 25
B. 35, 15
C. 15, 35
D. 40, 10
E. None of these

Sol. Lets assume no. of boys be 'x'
     And no. of girls be 'y'
Then, x + y = 50
Also, 12x + 8y = 500
Solving these two we get, x = 25 ; y = 25

3. One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A ball is transferred from the first bag to the second bag and then a ball is drawn from the second bag. Find the probability that ball drawn is white ?

A. 4/9
B. 3/9
C. 60/151
D. 5/9
E. None of these

Sol. Required Probability = (5/9)*(8/17) + (4/9)*(7/17) = 4/9.

4. 11,  31,   91,  271,  ?

A. 913
B. 813
C. 911
D. 811
E. None of these

Sol. 11*3 - 2 = 31
     31*3 - 2 = 91
     91*3 - 2 = 271
    271*3 - 2 = 811

5. 15, 16.4, 13.6, 17.8, 12.2, ?

A. 18.3
B. 20.2
C. 18.2
D. 19.2
E. None of these

Sol. 15 + (1.4*1) = 16.4
   16.4 - (1.4*2) = 13.6
   13.6 + (1.4*3) = 17.8
   17.8 - (1.4*4) = 12.2
   12.2 + (1.4*5) = 19.2

6. 18, 119, 708, ?, 14136, 42405

A. 3434
B. 3535
C. 3636
D. 3737
E. None of these

Sol. 18*7 -7 = 119
    119*6 -6 = 708
    708*5 -5 = 3535

7. 264, 262, 271, 243, ?

A. 302
B. 304
C. 306
D. 308
E. None of these

Sol. 264 – 1³ + 1 = 262
     262 + 2³ + 1 = 271
     271 – 3³ + 1 = 243

8. A can complete a work in 24 days, B in 30 days and C in 40 days. A worked for 3 days alone and then left. B took the remaining work and worked for 6 days alone and then left. C completed the remaining work alone. In how many days the whole work was completed ?

A. 27 days
B. 30 days
C. 32 days
D. 36 days
E. None of these

Sol. Work completed by A in 3 days = 3/24 = 1/8
     Work completed by B in 6 days = 6/30 = 1/5

Thus, remaining work to be completed by C = 1 - (1/8 + 1/5) = 27/40
So, (27/40)th is completed by C in = (27/40)*40 = 27 days.
Thus, total time to complete the work = (3 + 6 + 27) = 36 days.

9. What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?   

A. Rs. 400
B. Rs. 120
C. Rs. 510 
D. Rs. 220
E. None of these

Sol. Rate % = 100(568 - 520)/[520*7 - 568*5] = 6%
     Sum = (568 - 520)*100/[(7-5)*6] = Rs 400.

10. A bag contains 3 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both are black ?

A. 5/40
B. 6/40
C. 7/40
D. 8/40
E. None of these

Sol. The reqd. probability is 7C2 / 16C2 = 7/40.

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