Question

What will be the age of mac's father after 8 years if his present age is 10 years morebthan five - third of mac's present age and the sum of their ages is 90 years

Answer 1

GIVEN :

• Mac's father's age is 10 years more than 5/3 of Mac's present age.
• Sum of their age is 90 years.

TO FIND :

• Mac's father's age after 8 years.

SOLUTION :

We know that,

• Mac's father is 5/3 more than 10 years than Mac's present age.

So,

Let's assume that Mac's present age is x years.

Then,

Mac's father's age will be :

$\red \leadsto \bf \frac{5x}{3} + 10$

The equation formed :

$\implies \bf \frac{5x}{3} + 10 + x = 90$

According to the question,

$\bf \implies \: x + \frac{5x}{3} = 90 - 10$

$\bf \implies \: \frac{3x + 5x}{3} = 80$

$\bf \implies \: \frac{8x}{3} = 80$

$\bf \implies \: x = \frac{ \cancel{80} \times 3}{\cancel8}$

$\bold \gray \dag { \underline{ \boxed{\bf \orange{ \therefore \: x = 30 \: years}}}}\bold \gray \dag$

THEREFORE,

Mac's present age is x = 30 years.

And,

Mac's father's age is $\tt \leadsto \frac{5x}{3} + 10$

$\tt \leadsto \frac{5 × \cancel{30}}{\cancel3} + 10$

$\tt {\red {\leadsto { \blue{50 + 10}}}}$

$\bold\gray \dag{\underline{\boxed{\bf {\green {60 years.}}}}}\bold\gray \dag$

HENCE,

Required answer :

Age after 8 years will be 60 + 8 :

$\longrightarrow\bold\gray \dag {\underline{\boxed{\bf {\orange{ 68 years \:\:ans. \blue \checkmark }}}}}\bold\gray \dag$

Verification :

• Verification needs to be L. H. S. = R. H. S. by substituting the value of x.

Thereafter,

Substituting the value of x in the equation :

$\implies \bf \frac{5x}{3} + 10 + x = 90$

$\implies \bf \frac{5 × 30 }{3} + 10 + x = 90$

$\bf \implies \: \frac{5 \times\cancel{30}}{ \cancel3} + 10 + 30 = 90$

$\bf \implies \: 50 + 10 + 30 = 90$

$\bold\gray \dag{ \underline{ \boxed{\bf \green{\therefore 90 = 90}}}} \bold\gray \dag$

AFTERALL,

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

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