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1. If (5a + 3b) / (2a - 3b) = 23/5 , then the value of a : b is

A. 2 : 1

B. 1 : 4

C. 1 : 2

D. 4 : 1

**Answer : ****4 : 1**

Cross multiplying, 25a + 15b = 46a – 69b

--> 21a = 84b

--> a = 4b

--> (a/b) = (4/1)

--> a:b = 4:1

2. If two numbers are in the ratio 6 : 13 and their least common multiple is 312, then the sum of the numbers is

A. 75

B. 57

C. 76

D. 67

**Answer : ****76**

Let the numbers be 6k and 13k.

Given, L.C.M. = 312

L.C.M. of 6k and 13k = 6 × 13 × k

Then, 6 × 13 × k = 312

k = 4.

Substituting in 6k and 13k, Numbers are 24 and 52.

Sum = 24 + 52 = 76

3. A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.

A. 8 Liters

B. 10 Liters

C. 18 Liters

D. 22 Liters

**Answer : ****10 Liters**

Let the quantity of alcohol and water be 4x liters and 3x liters respectively. Then,

Given ► 4x / 3x

After five liters of water added => 4x / (3x + 5)

ஃ 4x / (3x + 5) = 4 / 5

20x = 12x + 20

x = 2.5

quantity of alcohol = 4x = 4 x 2.5 = 10

4. The ratio of three numbers is 3: 4: 5 and the sum of their squares is 1250. The sum of the numbers is:

A. 20

B. 40

C. 50

D. 60

**Answer : ****60**

Let the Numbers be 3x, 4x, and 5x then,

The sum of their squares = 9x^{2} + 16x^{2} + 25x^{2} = 1250

= 50x^{2} = 1250

= x^{2} = 25 ► x = 5

Sum of numbers = (3x + 4x + 5x) = 12x

= (12 x 5) = 60.

5. If 3:2 is the ratio of radius of two right circular cones and 1:1 is the ratio of their volumes. Then what will be the ratio of their heights ?

A. 1:3

B. 2:3

C. 7:2

D. 4:9

**Answer : ****4:9**

Given, Ratio of radius = 3:2

Let their radius be 3X and 2X.

Given, 1:1 is the ratio of their volume which means that they have equal volume.

Let h and H be their respective heights.

For a circular cone with radius R and height h, the formula for volume becomes

V = 1/3 x πr^{2} x h

So,

1/3 x π(3X)^{2} x h = 1/3 x π(2X)^{2} x H

9 h = 4 (H)

h / H = 4 / 9.

Hence required ratio is 4:9.

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