Question

Solve the Following Word Problem.
Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years ago was 4 times the age of Savita. Find their present ages.

Answer 1

Suppose the present age of Manish is x years and Savita be y years.

According to the first condition, the sum of their present ages is 31

∴ x + y = 31  .......(i)

Three years ago

Age of Manish = (x – 3) years

Age of Savita = (y – 3) years

According to the second condition, 3 years ago Manish's age was 4 times the age of Savita's.

∴ (x – 3) = 4(y – 3)

∴ x – 3 = 4y – 12

∴ x – 4y = – 12 + 3

∴ x – 4y = – 9  ......(ii)

Subtracting equation (ii) from equation (i), we get

  x + y = 31
x – 4y = – 9
–  +      +      
     5y = 40

∴ y = `40/5`

∴ y = 8

Substituting y = 8 in equation (i),

∴ x + y = 31

∴ x + 8 = 31

∴ x = 31 – 8

∴ x = 23

∴ Present age of Manish is 23 years and Savita is 8 years.