Question

After 15 years Ramesh’s age will be 5 times his age 5 years ago. What is the present age of Ramesh?
A) 5 years B) 10 years C) 15 years D) 20 years

Answer 1

QUESTION:-

After 15 years Ramesh’s age will be 5 times his age 5 years ago. What is the present age of Ramesh?

A) 5 years B) 10 years C) 15 years D) 20 years

EXPLANATION:-

Let the present age of ramesh =x years

After 15 years his age=x+15

Ramesh age 5 years age=x-5

ATQ,

x+15=5x−25

15=4x-25

15+25=4x

4x=40

x=10

So the present age of ramesh is 10 years

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Answer 2

Given : After 15 years, Ramesh’s age will be 5 times his age 5 years ago.

To Find : The present age of Ramesh?

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❍ Let us assume that, the present age of Ramesh is 'x'. After 15 years, age of Ramesh = x + 15. And age of Ramesh 5 years ago = x - 5.

$\boldsymbol{\underline{According \: to \: the \: question,}}$

$\sf{ \leadsto \: x + 15 = 5(x - 5) }$

$\sf{ \leadsto \: x + 15 = 5x - 25}$

$\sf{ \leadsto \: 15 + 25 = 5x - x}$

$\sf{ \leadsto \: 4x = 40}$

$\sf{ \leadsto \: x = \cancel\dfrac{40}{4} }$

$\purple{\sf{ \leadsto \: x = 10}}$

Hence, the present age of Ramesh is 10 years.

ㅤ

So, option (B) 10 years is correct. ✓

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Verification :

$\tt{ \leadsto \: x + 15 = 5(x - 5) }$

❐ Substituting x = 10, we get

$\sf{ \leadsto \: 10 + 15 = 5(10 - 5) }$

$\sf{ \leadsto \: 25 = 50 - 25}$

$\sf{ \leadsto \: 25 = 25}$

$\red{\sf{ \leadsto \: LHS = RHS}}$

Hence, verified. ✓