Question

Rajesh is 24 years older than Mukesh 10 years back Rajesh age was five times the age of Mukesh find their ages ​

Answer 1

GIVEN :

• Rajesh is 24 years older than Mukesh.

TO FIND :

• The age of both i.e., Rajesh and Mukesh after solving the above according to the statement.

SOLUTION :

We know that,

• Rajesh is 24 years older than Mukesh.

• So, lets assume that the age of Mukesh is x years.

Thereafter,

• Rajesh's age will be (x + 24) years. as he is 24 years older.

Again,

• It is also being told that 10 years ago Rajesh was five times the age of Mukesh.

Hence,

10 years ago their ages :

(x - 10) years and (x + 24) - 10 years.

Five times the age of Mukesh :

The equation formed :

$\bf \implies \: 5(x - 10) = (x + 24) - 10$

According to the question,

$\bf \implies \: 5x - 50 = x + 24 - 10$

$\bf \implies \: 5x - 50 = x + 14$

$\bf \implies \: 5x - x = 50 + 14$

$\bf \implies \: 4x = 64$

$\bf \implies \: x = \frac{ \cancel{64}}{ \cancel4}$

$\bold \green \dag { \underline{ \boxed{\bf \therefore {\orange{ x = 16 \: years}}}}} \bold \green \dag$

HENCE,

Mukesh's age is x = 16 years.

And,

Rajesh's age is (x + 24) years :

= 16 + 24 = 40years.

Verification :

• Verification needs the L. H. S. = R. H. S. by substituting the value of x in the equation :

5(x - 10) = (x + 24) - 10

Thereafter,

Substituting the value of x

$\bf \implies \: 5x - 50 = x + 14$

$\bf \implies \: (5 \times 16) - 50 = 16 + 14$

$\bf \implies \: 90 - 50 = 30$

$\bold\blue \dag{ \underline{ \boxed{\bf \orange{\therefore 30 = 30}}}} \bold\blue \dag$

AFTERALL,

L. H. S. = R. H. S

$\bold \red \dag { \underline{\boxed{ \green{\bf Hence,\purple V \red e \orange r \pink i \blue f \green i \red e \pink d : -}}}} \bold \red \dag$

NOTE :

Read it carefully.