A. 2: 3
B. 3: 5
C. 5: 10
D. 10: 15

## The sum of three numbers is 98. If the ratio of the first to the 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

### Solution

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.

## Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is?

A. 2: 5
B. 3: 5
C. 4: 5
D. 6: 7

### Solution

Let the third number be x.
Then, first number = 120% of x = 120x/100 = 6x/5 second numbet = 150% of x = 150x/100 = 3x/2 Ratio of first two numbers = 6x/5 : 3x/2 =12x : 15x = 4 : 5.

## Find the fourth proportion to 3, 7 and 9.

A. 63
B. 31
C. 21
D. 27

### Solution

3:7::9:x 3x=7*9=63 x=21

## A:B=2:3, B:C=3:4, A:D=4:5. Find C:D.

A. 2:5
B. 4:5
C. 6:5
D. 8:5

### Solution

A:C=(A:B)*(B:C) =(2/3)*(3/4)= 1/2 C:D=(C:A)*(A:D) =(2)*(4/5) = 8:5

## The number of seats available for Biology and Computer Science in a school is in the ratio 5:8. They are to be increased by 30% and 25% . Find the new ratio.

A. 6:10
B. 13:20
C. 3:4
D. 35:33

### Solution

Let the number of seats be 5x and 8x. New ratio
= (1.3*5x):(1.25*8x)
= 6.5x:10x
= 13:20

## Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2.

A. 38
B. 35
C. 10
D. 28

### Solution

Let z = 4y-1
When x = 14, y = 2, z = (4*2) – 1 = 7
Now, x varies directly as z = 4y-1
When y = 5, z = (4*5) – 1 = 19
x 14 7
y – 19
Therefore, x = (14*19)/7 = 38

## The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.

A. 4
B. 6
C. 3
D. 2

### Solution

Let the numbers be 2x and 3x. (2x)³+(3x)³=280 8x³+27x³=280 35x³=280 x³=8 x=2 The numbers are 4 and 6.

## The sum of three numbers is 172. The ratio of the first and second numbers is 8:11. The ratio of the second and third is 5:7. Find the second number.

A. 44
B. 55
C. 66
D. 77

### Solution

Let the numbers be a, b and c. a+b+c = 172 a:b = 8:11 b:c = 5:7 11a = 8b a = 8b/11 7b = 5c c = 7b/5 (8b/11)+b+(7b/5) = 172 40b+55b+77b = 172*55 172b = 172*55 b=55

A. 9:19
B. 19:9
C. 15:28
D. 28:15