Question

The sum of Manisha and Savita's present age is 31 years. 3 years ago, Manisha was about four times the age of Savita. So find out the age of both of them today.​

Answer 1

Let the -

• the present age of Manisha is "M" years.

According to question,

⇒ M + N = 31 ....(1)

⇒ M - 3 = 4[(31 - M) - 3] ....(2)

The sum of ages of Manisha and Savita is 31 years.

As the age of Manisha is "M" years.

$\therefore$ Age of Savita = Sum of their ages - Present age of Manisha

→ (31 - M) years

Also,

$\bold{3\:years\:ago} \begin{cases} \sf{Age\: of \:Manisha = (M - 3) years} \\ \sf{Age\: of \:Savita = (31 - M - 3) = (28 - M) years} \end{cases}$

3 years ago, Manisha was about four times the age of Savita.

→ M - 3 = 4(28 - M)

→ M - 3 = 112 - 4M

→ M + 4M = 112 + 3

→ 5M = 115

→ M = 23

From above calculations M = 23.

So, Present age of Manisha = 23 years.

$\therefore$ Present age of Savita = Sum of their ages - Present age of Savita

i.e.

→ 31 - M

Substitute the age of Manisha (M = 23) above. To find the age of Savita.

→ 31 - 23

→ 8

So, the present age of Savita = 8 years

•°• Present age of Manisha is 23 years and the present age of Savita is 8 years.

Verification :

From the above calculations, we have M = 23.

Also,

The present age of Manisha + Present of Savita = 31 years.

• The present age of Manisha = 23 years
• The present age of Savita = 8 years

→ (23 + 8) years = 31 years

→ 31 years = 31 years

Answer 2

$\bold{\underline{\underline{\huge{\sf{UtTar:}}}}}$

Present age of Manisha = 23 years

Present age of Savita = 23 years

$\bold{\underline{\underline{\large{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

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

To FiNd :

• Present age of Manisha
• Present age of Savita

SoLuTiOn :

Let the present age of Manisha be x years.

Let the present age of Savita be y years.

$\sf{\underline{\underline{As\:PeR\:tHe\:FiRsT\:cOnDiTiOn}}}$

• Sum of their present ages = 31

Constituting it mathematically,

$\longmapsto$$\sf{x\:+\:y\:=\:31}$ ----> (1)

$\sf{\underline{\underline{As\:PeR\:tHe\:SeCoNd\:cOnDiTiOn}}}$

• 3 years ago, Manisha was about four times the age of Savita.

Age 3 years ago :

Manisha = x - 3 years

Savita = y - 3 years

Constituting it mathematically,

$\longmapsto$$\sf{x\:-\:3\:=\:4\:(\:y\:-\:3}$

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

$\longmapsto$$\sf{x\:-\:4y\:=\:-\:12\:+3\:}$

$\longmapsto$$\sf{x\:-\:4y\:=\:-\:9}$ ---> (2)

Solve equation 1 and equation 2 simultaneously by elimination method.

Subtractt equation 2 from equation 2,

x + y = 31

x - 4y = - 9

_________

5y = 40

$\longmapsto$$\sf{y\:=\:{\dfrac{40}{5}}}$

$\longmapsto$$\sf{y\:=\:8}$

Substitute y = 8 in equation 1,

$\longmapsto$$\sf{x\:+\:y\:=\:31}$ ----> (1)

$\longmapsto$$\sf{x\:+\:8\:=\:31}$

$\longmapsto$$\sf{x\:=\:31\:-\:8}$

$\longmapsto$$\sf{x\:=\:23}$

•°• Present age of Manisha = 23 years

Present age of Savita = 8 years