1. Three friends X, Y, Z invested in a business in the ratio of 4:5:6. After 6 months Z withdraw half of his capital. If the sum invested by X is 36000, then the profit earned by Z out of the total profit of 60000 ?
A.20000
B.30000
C.40000
D.50000
E.None of these
Sol. Sum invested by X = 4x = 36000.
X = 9000
Investment made by X, Y , Z – 36000, 45000, 54000
Ratio in which the profit will divide- 36000*12 : 45000*12 :(54000*6 + 27000*6)
i.e 4:5:9. So Z share = (9/18)*60000 = 30000
2. Twice the speed downstream is equal to the thrice the speed upstream, the ratio of speed in still water to the speed of the current is:
A. 1 : 5
B. 5 : 1
C. 1 : 3
D. 2 : 3
E. None of these
Sol. Let, speed in still water = x Km/h.
Speed of current = y Km/h.
Speed downstream = (x + y) Km/h.
Speed upstream = (x – y) Km/h.
2(x + y) = 3(x – y)
x = 5 y
or, x/y=5/1 or 5 : 1.
3. Karan decided to donate 5% of his salary. On the day of donation, he changed his mind and donated Rs. 1687.50 which was 75% of what he had decided earlier. How much is Karan's salary?
A. Rs. 37.500
B. Rs. 45,000
C. Rs. 33,750
D. Cannot be determined
E. None of these
Sol. Karan donated = (5*75)/100=15/4%
Then, 15/4 % = 1687.50
Karan's salary = [(1687.50*4)/15]*100=45000
4. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
A. 8, 20, 28
B. 16, 28, 36
C. 20, 35, 45
D. 25, 30, 40
E. None of these
Sol. Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56 => 20x = 80 => x = 4.
Their present ages are 16 yrs, 28 yrs. and 36 yrs. respectively.
5. The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages is 34. Find the present age of father.
A. 32 years
B. 36 years
C. 38 years
D. 40 years
E. 39 years
Sol. Let the ages of father and son be x and (45 – x) years respectively.
Then, (x – 5) (45 – x – 5) = 34
(x – 5) (40 – x) = 34 => x2 – 45x + 234 = 0
(x – 39) (x – 6) = 0 => x = 39 or x = 6.
Father’s age = 39 years and son’s age = 6 years
6. A box contains 3 red, 6 blue,2 green and 4 yellow balls. If two marbles are picked randomly then the probability that either both are red or both are green is ?
A. 3/5
B. 4/105
C. 2/7
D. 5/91
E. None of these
Sol. P(E) = (3C2 + 2C2)/15C2 = 4/105.
7. The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is:
A. 5%
B. 6(2/3)%
C. 6%
D. 7(1/5)%
E. None of these
Sol.Let the sum of money be P
I = (P×R×T)/100
(4/9)P = (P×R×T)/100
R = √(400/9) = 20/3 = 6(2/3)%.
8. What would be the compound interest accrued on an amount of 8000 at the rate of 15% per annum in three years ?
A. 4283
B. 4051
C. 4167
D. 4325
E. None of these
Sol. CI =8000[(1+15/100)^3-1]
= 8000[(115/100)^3-1] = 4167.
9. The circumference of base of a circular cylinder is 6Ï€ cm. The height of the cylinder is equal to diameter of the base. Maximum amount of water that can be poured in the cylinder is
A. 54Ï€ cm3
B. 36Ï€ cm3
C. 0.054Ï€ cm3
D. 0.54Ï€ cm3
E. None of these
Sol. Given 2Ï€r = 6Ï€
r = 3
h = 2*3 = 6
V = Ï€r2h = Ï€×3×3×6 = 54 Ï€.
10. Two vessels contain milk and water in the ratio 3 : 2 and 7 : 3. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 2 : 1.
A. 2 : 1
B. 1 : 2
C. 4 : 1
D. 1 : 4
E. None of the above
Sol. = (21 - 20)/30
= (10 - 9)/15
= 1/30 = 1/15
Required ratio = 1/30 : 1/15 = 1:2.
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