Question

12.) Two numbers are in the ratio 7:11. If 7 is added to each of the numbers, the ratio becomes 2:3. find the numbers.​

Answer 1

Answer :-

Given :-

• Ratio of two numbers is 7 : 11
• After adding 7 to both, ratio becomes 2 : 3

To Find :-

• Numbers

Solution :-

Let the numbers be 7x and 11x.

After adding 7 :-

→ New numbers = 7x + 7 and 11x + 7

According to the question :-

→ ( 7x + 7 ) / ( 11x + 7 ) = 2 / 3

→ 3 ( 7x + 7 ) = 2 ( 11x + 7 )

→ 21x + 21 = 22x + 14

→ 22x - 21x = 21 - 14

→ x = 7

Numbers are :-

• 7x = 7 × 7 = 49
• 11x = 11 × 7 = 77

Numbers are 49 and 77

Verification :-

Ratio of numbers = 49 : 77

= 7 : 11

Adding 7 to both numbers :-

→ 49 + 7 = 56

→ 77 + 7 = 84

Ratio of new numbers = 56 : 84

= 2 : 3

Hence, our answer is correct.