Question

The sum of present ages manisha &savita is 31 years 3 years ago manisha age was 4 time savita age . find their present age

Answer 1

Answer:

Age of savita= 23

Age of manisha= 8

Step-by-step explanation:

Answer is given in the attachment

Answer 2

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  )

              $\boxed{\pink{x + y = 31 }}$

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)

             $\boxed{\pink{x = 4y - 9}}$

Let's use Equation 2 in Equation 1 ,

(4y - 9) + y = 31

⇒ 4y - 9 + y = 31  

⇒ 5y = 31 + 9  

⇒ 5y = 40  

⇒ y = 8

                   $\boxed{\pink{y = 8}}$

Using this value of 'y' in Equation 2 ,

x = 4 × (8) - 9

⇒ x = 32 - 9

⇒ x = 23

                $\boxed{\pink{x = 23}}$

   

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