Question

Sum of the present ages of Manish and Savita is 31. Manish age 3 years ago was
4 times the age of Savita. Frame the equations?​

Answer 1

Solution :

Let Manish's present age be m years and

Savita's present age be s years

Given :

$\bullet \sf \: m + s = 31 \: years....(i)$

3 years ago :

• Manish's age = m - 3

• Savita's age = 4 (s - 3)

According to the question:

$\longrightarrow \sf \: (m - 3) = 4(s -3)....(ii)$

From equation (i) value of m = 31-s

Putting m = 31-s in equation (ii)

$\longrightarrow \sf \: (m - 3) =4 (s - 3)$

$\longrightarrow\sf \: 31 - s - 3 = 4s - 12$

$\longrightarrow\sf \: 28 - s = 4s - 12$

$\longrightarrow\sf \: 28 + 12 = 4s + s$

$\longrightarrow\sf \: 40 = 5s$

$\longrightarrow\sf \: s = \dfrac{40}{5}$

$\longrightarrow\sf \: s = \large \boxed{ \red{ \sf \: 8 \: years}}$

Putting the value of s = 8 in equation (i)

$\bullet \sf \: m + s = 31 \: years$

$\longrightarrow \sf \: m + 8 = 31 \: years$

$\longrightarrow \sf \: m = 31 - 8 \: years$

$\longrightarrow \sf \: m = \large \boxed{ \red{ \sf \: 23 \: years}}$

Hence,

• Manish's age = 23 years

• Savita's age = 8 years

Answer 2

AnsweR :

$\bf{\Large{\underline{\sf{Given\::}}}}}$

Sum of the present ages of Manish and Savita is 31. Manish age 3 years ago was 4 times the age of Savita.

$\bf{\Large{\underline{\sf{To\:find\::}}}}}$

Their ages.

$\bf{\Large{\underline{\rm{\green{Explanation\::}}}}}$

Let the present age of Manish be R years.

Let the present age of Savita be M years.

A/q

$\implies\sf{R+M=31}\\\\\\\implies\sf{\red{R\:=\:31-M................(1)}}$

Now,

$\bf{\Large{\boxed{\sf{3\:years\:AgO\::}}}}}$

$\leadsto\sf{Manish\:age\:=\:(R-3)\:years}\\\\\\\leadsto\sf{Savita\:age\:=\:(M-3)\:years}$

So,

$\implies\sf{R-3=4(M-3)}\\\\\\\implies\sf{31-M-3=4M-12\:\:\:\:\:\:\:\:\:\:\:\bigg[From\:equation\:(1)\bigg]}\\\\\\\implies\sf{28-M\:=\:4M-12}\\\\\\\implies\sf{-M-4M\:=\:-12-28}\\\\\\\implies\sf{-5M\:=\:-40}\\\\\\\implies\sf{M\:=\:\cancel{\dfrac{-40}{-5} }}\\\\\\\implies\sf{\red{M\:=\:8\:years}}$

$\bigstar$Putting the value of M in equation (1), we get;

$\implies\sf{R\:=\:31-8}\\\\\\\implies\sf{\red{R\:=\:23\:years}}$

Thus,

$\bigstar$The present age of Manish is 23 years.

$\bigstar$The present age of Savita is 8 years.