Answer
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1. In a covering, a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
Answer: Option 3
Solution
Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x – 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
2. A train 110 m long is running with a speed of 60 km/hr. At what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Answer: Option 2
Solution
Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
3. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Answer: Option 2
Solution
C’s 1 day’s work = 1/3 – (1/6 + 1/8) = 1/3 – 7/24 = 1/24
A’s wages : B’s wages : C’s wages
1/6 : 1/8 : 1/24 = 4:3:1
C’s share = 1/8 * 3200 = Rs. 400
4. A, B, and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Answer: Option 5
Solution
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 – 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
5. If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?
Answer: Option 2
Solution
(A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 510 * 2/17 = Rs. 60
B’s share = 510 * 3/17 = Rs. 90
C’s share = 510 * 12/17 = Rs. 360.
6. The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Answer: Option 3
Solution
S = 4
M = x
DS = x + 4
US = x – 4
6/(x + 4) + 6/(x – 4) = 2
x = 8
7. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
Answer: Option 1
Solution
et sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10%
Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.
8. Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
Answer: Option 2
Solution
2 * 22/7 * 14 = 88
88 * 1 1/2 = Rs.132
9. A pupil’s marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
Answer: Option 3
Solution
Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2
x/2 = (83 – 63) => x/2 = 20 => x = 40.
10. The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is?
Answer: Option 3
Solution
Other number = (11 * 7700)/275 = 308.
11. If the sum of the two numbers is 22 and the sum of their squares is 404, then the product of the numbers is?
Answer: Option 1
Solution
Let the numbers be x and y.
Then, (x + y) = 22 and x2 + y2 = 404
Now,
2xy = (x + y)2 – (x2 + y2)
2xy= 222 – 404 = 484 – 404 = 80
xy = 40
12. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Answer: Option 2
Solution
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
13. The principle that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Answer: Option 4
Solution
Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
14. If the height of a cone is increased by 100% then its volume is increased by?
Answer: Option 1
Solution
100%
15. Find the one which does not belong to that group?
Answer: Option 4
Solution
Walk, Talk, Drink and Lick are verbs, but not Plank.
16. A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of the bicycle for A is?
Answer: Option 4
Solution:
125% of 120% of A = 225
125/100 * 120/100 * A = 225
A = 225 * 2/3 = 150.
17. A person’s present age is two-fifths of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
Answer: Option 3
Solution
Let the mother’s present age be x years. Then, the person’s present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
18. In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
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