Question

Sum of the present ages of Manisha
and Savita is 31. Manisha's age 3
years ago was 4 times the age of
Savita. Find their present age.
cManisha and​

Answer 1

Given:

• The sum of the present ages of Manisha and Savita is 31.
• Manisha's age 3 years ago was 4 times the age of Savita.

To find: Their present ages.

Answer:

Let 'x' and 'y' be the present ages of Manisha and Savita respectively.

According to the first statement,

x + y = 31  ↔  Equation 1

Manisha's and Savita's ages 3 years ago would've looked like this:

• x - 3
• y - 3

According to the second statement,

x - 3 = 4(y - 3)

x - 3 = 4y - 12

x - 4y = -12 + 3

x - 4y = -9  

x = 4y - 9  ↔  Equation 2

Let's use Equation 2 in Equation 1.

(4y - 9) + y = 31

4y - 9 + y = 31

5y = 31 + 9

5y = 40

y = 8

Using this value of 'y' in Equation 2,

x = 4 × (8) - 9

x = 32 - 9

x = 23

Therefore, Manisha's and Savita's ages are 23 years and 8 years respectively.