Question

A number is divided into two parts in the ratio of 5 ∶ 6 respectively. The sum of 60 percent of first part and 50 percent of second part is 84. If both parts are increased by 10, then what will be the respective ratio between the sum of old numbers and new numbers? 
1. 71 ∶ 87
2. 73 : 87 
3. 77 : 87 
4. 75 : 87

Answer 1

Correct Answer - Option 3 : 77 : 87 

Given:

The number is divided in the ratio of 5 : 6

Calculation:

Let the first part be 5x and the second part be 6x.

So, 

60% of 5x + 50% of 6x = 84

( ( 60 / 100 ) × 5x ) + ( ( 50 / 100 ) × 6x ) = 84

3x + 3x = 84 

x = 84 / 6 = 14 

∴ First part = 5x = 5 × 14 = 70

Second part = 6x = 6 × 14 = 84

The old umber will be 70 + 84 = 154

When the two parts are increased by 10.

First part = 5x + 10 

= ( 5 × 14 ) + 10 = 70 + 10 = 80

Second part = 6x + 10

= ( 6 × 14 ) + 10 = 84 + 10 = 94

∴ The new number obtained is 174

The ratio of the old number to the new number is 

154 / 174 = 77 / 87

∴ The ratio of the old number to the new number is 77 : 87