Question

i. 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

Answer:

Given :

$\textsf{Sum of the ages of Manish and Savita = 31}$

$\textsf{Manish 's age 3 years ago was 4 times the age of Savita}$

To find :

$\textsf{Their present age of Manish and Savita}$

Concept :

Let the age of the Manish be x

And let the age of the Savita be y

So , sum of their ages is 31 :

$\sf{x + y = 31}$

$\sf{x=31-y}$ .............. (i) Taken as equation 1.

So after 3 years ago :

Their ages will like this :

Manish age = (x-3)

And Savita age = 4(y-3)

So , to find their age use this equation :-

$\sf\boxed {x-3=4(y-3)}$

Solution :

$\sf\implies {x-3=4(y-3)}$

Used cross multiplication to find y-3 .

$\sf\implies {x-3=4y-12}$

Putting x as the value of equation (i)

$\sf\implies {31-y-3=4y-12}$

$\sf\implies {31-3+12=4y+y}$

$\sf\implies {(31+12)-3=5y}$

$\sf\implies {43-3=5y}$

$\sf\implies {40=5y}$

$\sf\implies {\dfrac{40}{5}=y}$

$\sf\implies {8=y}$

So , the age of Savita is 8 years .

Manish age :

Putting the value of y at the equation (i)

$\sf\implies {x=31-y}$

$\sf\implies {x=31-8}$

$\sf\implies {x=23}$

So , the age of Manish is 23 years .

Answer :

Present age of Manish = 23 years

Present age of Savita = 8 years