1. Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both the pipes are opened to fill the tank but when the tank is one-third full a leak develops in the tank through which one-third of the water supplied by both the pipes leaks out. What is the total time taken to fill the tank?
A. 12 hrs
B. 18 hrs
C. 26 hrs
D. 14 hrs
E. None of these
Sol. Let total capacity of pipe = 60
Efficiency of 1st pipe = 3
And efficiency of IInd pipe = 2
i.e. 1/3rd part of tank fill in [(1/3)60]/5 = 4 hr
Now, after the leak, the tank is filled at the rate of = (5)-(5/3) = 10/3
Remaining 40 L will fill in [40/(10/3)]= 12 hr
Total time = (4+12 hr) = 16 hr.
2. A bag contains 8 white and 9 black balls. Balls are drawn one by one. Two balls are drawn without replacement. What is the probability that one is white and other is black?
A. 8/15
B. 1/17
C. 8/17
D. 1/15
E. 9/17
Sol. P= (8C1*9C1)/(17C2) = 8/17.
3. In an Examination, Amitosh secured 60% marks and passed by 40 marks while Karun scored 40% marks and failed by 60 marks . Vijay scored 90 marks more than the passing marks. What was the Vijay’s percentage of marks obtained by him ?
A. 70%
B. 74%
C. 80%
D. 75%
E. 72%
Sol. Total be 100x and Passing marks be y
Karun scored 40% marks and failed by 60 marks = 40x+60 = y
Amitosh secured 60% marks and passed by 40 marks= 60x - 40 = y
Solving x = 5, and y = 260.
So Vijay scored 260 + 90 = 350
(350/500) * 100 = 70%.
4. In a race of 100 meter , Rajiv beats Ajay by 40 meters , and Ajay beats Dhawan by 40 meters .If Rajiv completes the race in 9 seconds after how much time does Dhawan complete the race ?
A. 15 sec
B. 14 sec
C. 25 sec
D. 20 sec
E. None of these
Sol. When Rajiv runs 100m Ajay runs 60 m
Ratio of speeds = 5 : 3
Ratio of speeds of Ajay and Dhawan = 5 : 3
Ratio of their three Speeds = 25 : 15 : 9
Time is inverse to speed , So
1/25 : 1/15 : 1/9
9 : 15 : 25
Dhawan finishes in 25 seconds.
5. Akshay started a business with an investment of Rs.72000. After X months Bikram joins Arya with a capital of Rs.36000. If the ratio of profit at the end of the year is 3:1, then X is
A. 8 months
B. 6 months
C. 4 monhs
D. 5 months
E. None of these
Sol. 72000 * 12/36000 * (12-X) = 3 / 1
On solving we get, X = 4 months.
6. A , B and C entered into a business partnership in the ratio of 3 : 5 : 2 respectively. At the end of the year, they earned a profit of Rs.60,000 which is 15% of their total investment. What is the share of B in the investment ?
A. 2,00,000
B. 3,00,000
C. 1,00,000
D. 4,00,000
E. 5,00,000
Sol. 15 % = 60,000.
100% = 4,00,000.
B’s share = 5/10 * 4,00,000 = Rs.2,00,000.
7. Among the three number the first is thrice the third number and second number is half of the first number. If the average of the three number is 80 then find the third number ?
A. 43.63
B. 43.67
C. 44.56
D. 43.69
E. None of these
Sol. Let third num. = x, 1st num. = 3x, second no. = 3x/2
[3x+(3x/2)+x] / 3 = 80
11x/2 = 240
X = (2×240) / 11 = 43.63.
8. 8, 17, 48, 121, ?
A. 262
B. 202
C. 203
D. 562
E. None of these
Sol. 8 + 1^2+2^3 = 17
17 + 2^2+3^3 = 48
48 + 3^2+4^3 = 121
121 + 4^2+5^3 = 262
9. 584, 588, 580, 592, ?
A. 560
B. 576
C. 550
D. 500
E. None of these
Sol. +4 -8 +12 -16
10. 5, 3.5, 7.25, 21.125, ?
A. 77.9375
B. 73.9175
C. 71.8855
D. 72
E. None of these
Sol. *0.5+1 *1.5+2 *2.5+3 *3.5+4
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