Question

seven years ago the ratio of the age of sonu and Suresh was 3:4 .
9 years hence the ratio of their age 7:8 respectively what is the present age of Suresh?​

Answer 1

Given:

• Seven years ago the ratio of the age of Sonu and Suresh was 3 : 4
• 9 years hence the ratio of their age 7 : 8 respectively

To find: the present age of Suresh

Solution:

• Let the age of Sonu and Suresh be x and y respectively

• Seven years ago, their ages were (x - 7) years and (y - 7) respectively.

By the given condition,

(x - 7) : (y - 7) = 3 : 4

or, (x - 7) / (y - 7) = 3 / 4

or, 4x - 28 = 3y - 21

or, 4x - 3y = 7 ... ...(i)

• Nine years hence, their ages will be (x + 9) years and (y + 9) years respectively.

By the given condition,

(x + 9) : (y + 9) = 7 : 8

or, (x + 9) / (y + 9) = 7 / 8

or, 8x + 72 = 7y + 63

or, 8x - 7y = - 9 ... ...(ii)

We have two equations:

• 4x - 3y = 7 ... ...(i)
• 8x - 7y = - 9 ... ...(ii)

Multiplying (i) by (2) and subtracting from (ii), we get

• 8x - 7y - 2 (4x - 3y) = - 9 - 2 * 7
• or, 8x - 7y - 8x + 6y = - 9 - 14
• or, - y = - 23
• or, y = 23

Putting y = 23 in (i), we get

• 4x - 3 * 23 = 7
• or, 4x - 69 = 7
• or, 4x = 7 + 69
• or, 4x = 76
• or, x = 19

Answer:

• Suresh is presently 23 years old.