Question

The sun of ages of Anup and his father is 100. When Anil is as old as his father now, he will be five times as old as his son Anuj now. Anuj will be eight years older than Anup is now, when Anup is as old as his father. What are their ages?​

Answer 1

AnswEr:

Let us Consider that the Anup age be x.

Then, His Father age = (100 - x).

Anuj's age = $\sf\:\dfrac{100\:-\:x}{x}$

$\dag\:\:\bold{\underline{\sf{\red{According\:to\: Question\:Now,}}}}$

$\longrightarrow\sf\:(100 - x) - x + \dfrac{100\:-\:x}{5} = x + 8$

$\longrightarrow\sf\:\dfrac{100\:-\:x}{1} -\dfrac{x}{1} + \dfrac{100\:-\:x}{5} = x + 8$

$\longrightarrow\sf\:\dfrac{500 \:-\:5x\:-\:5x\:+\:100\:-\:x}{5} = x + 8$

$\longrightarrow\sf\: \dfrac{600\:-\:11x}{5} = x + 8$

$\dag\:\:\small{\underline{\sf{\red{Cross\: Multiplying}}}}$

$\longrightarrow\sf\:600 - 11x = 5(x + 8)$

$\longrightarrow\sf\:600 - 11x = 5x + 40$

$\longrightarrow\sf\:600 - 40 = 5x + 11x$

$\longrightarrow\sf\:560 = 16x$

$\longrightarrow\sf\: x = \dfrac{560}{16}$

$\longrightarrow\large{\underline{\boxed{\sf{\blue{x \:= \; 35}}}}}$

So, Anup age is 35 years.

$\rule{120}2$

Now, Finding Anup's Father Age

$\longrightarrow\sf\: 100 - x$

$\longrightarrow\sf\:100 - 35$

$\longrightarrow\large{\underline{\boxed{\sf{\blue{65}}}}}$

Anuj's Age

$\longrightarrow\sf\: \dfrac{100\:-\:35}{5}$

$\longrightarrow\sf\: \dfrac{65}{5}$

$\longrightarrow\large{\underline{\boxed{\sf{\blue{13}}}}}$

Hence, Anup's age = 35 years.

Anuj's age = 13 years.

And, Anup's Father age = 65 years.

Answer 2

$\mathfrak{\huge{\pink{ANSWER}}}$