1.
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
A. 8:9
B. 17:18
C. 21:22
D. 23:24
Answer: Option C
Explanation:
Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
=> [120/100 x 7x] and [110/100 x 8x]
=> 42x/5 and 44x/5
=> The required ratio = 42x/5 : 44x/ 5] = 21 : 22.
2.
There are 2 vessels which are filled with the pure components. Vessel 1 contains 20 litres of milk and vessel 2 contains 20 litres of water, 5 litre of milk is taken from the vessel 1 and replaced in vessel 2. Then 4 litres of mixture is transferred from vessel 2 to vessel 1. Find the ratio of amount of water in vessel 1 to the amount of milk in vessel 2?
A. 7: 8
B. 8:7
C. 16 : 21
D. none of these
Answer: Option C
Explanation:
When 5 litres of milk is transferred, amount of milk left in vessel 1 = 15 litres. Amount of milk & water in vessel 2 is 5 and 20 litres Now, 4 litres of mixture containing milk and water in the ratio 1: 4 is poured in pure milk of volume 15 litres. 4 litres of mixture contains 3.2 litres of water and 0.8 litres of milk. :. Amount of milk left in vessel 2 = 5 –0.8 = 4.2 litres. Ratio of water in vessel 1 to milk in vessel 2 = 3.2 : 4.2 = 16 :21
3.
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit’s salary?
A. Rs. 17,000
B. Rs. 20,000
C. Rs. 25,500
D. Rs. 38,000
Answer: Option D
Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, (2x + 4000)/ (3x + 4000)= 40/57
=> 57(2x + 4000) = 40(3x + 4000)
=>6x = 68,000
=> 3x = 34,000
Sumit’s present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000
4.
If 0.75 😡 :: 5 : 8, then x is equal to:
A. 1.12
B. 1.2
C. 1.25
D. 1.258
Answer: Option B
Explanation:
(x x 5) = (0.75 x 8) , x =6/5 = 1.20
5.
The present ages of three persons 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. None of these
Answer: Option B
Explanation:
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 4x = 16 years, 7x = 28 years and 9x = 36
6.
The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
A. 20
B. 30
C. 48
D. 58
Answer: Option B
Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 = [5 x 3/5] : [8 x 3/5] = 3: 24/5
=> A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24
=> B = [98 x 15/49] = 30
7.
There is a square of side 6cm . A circle is inscribed inside the square. Find the ratio of the area of circle to square.
A. 11/14
B. 12/14
C. 10/11
D. 13/14
Answer: Option A
Explanation:
Area of the square is 36.
Divide it into 4 so each square is 9.
So the side is 3.
Radius is 3
Area of the square is 36 and circle is pi*r^2 ie 28.26
The ratio is 11/14
8.
For every eight leaps of a hare, a cat takes five leaps, but very two leaps of the hare is equal to six leaps of the cat. What is the ratio of the speed of the hare to that of the cat?
A. 8 : 13
B. 24 : 5
C. 4: 7
D. 8: 15
Answer: Option B
Explanation:
2h= 6c=> h =3c
8h: 5c=> 24c : 5c=> 24 :5
9.
60 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 kms using 1200 cc engine?
A. 80 litres
B. 90 litres
C. 120 litres
D. 170 litres
Answer: Option C
Explanation:
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = (800/600) 60 = 80 litres.
The amount of diesel required varies directly as the engine capacity.
Therefore, with a 1200 cc engine, quantity of diesel required =(1200/800)*80 = 120 litres.
10.
If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
A. 1
B. 7/2
C. 7
D. 49
Answer: Option C
Explanation:
Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders 1 : 7
Webs 7 :1 } :: 7 : x
=> 1 x 7 x x = 7 x 1 x 7
=> x = 7.