Question

a grandfather is 8 times as old as his grandson. also, he is 63 years older than him. find their present age.​

Answer 1

$\sf \underline {Answer : }$

• Age of grandson = 9 years
• Age of grandfather = 72 years

Given :

• the grandfather is 8 times as old as his grandson.
• age of grandfather is 63 years more than that of grandson.

To find :

• their present age.  

Solution :

➝ Let's find their present age.

• Let the age of grandson be x and the age of grandfather be 8x. And the age of grandfather is 63 years more than age of grandson, hence :

→ 8x = x + 63

→ 8x - x = 63

→ 7x = 63

→ x = 63/7

→ x = 9 years

Present age of grandfather = 8x

= 8 × 9 = 72 years

Present age of grandson = x

= 9 years

• Therefore, the ages of grandfather and grandson are 63 years and 9 years respectively.

Answer 2

Answer:

Given :-

• A grandfather is 8 times as old as his grandson.
• He is 63 years older than him.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Grandson)} =\: a\: years$

$\mapsto \bf Present\: Age_{(Grandfather)} =\: 8a\: years$

According to the question,

$\implies \sf a + 63 =\: 8a$

$\implies \sf a - 8a =\: - 63$

$\implies \sf {\cancel{-}} 7a =\: {\cancel{-}} 63$

$\implies \sf 7a =\: 63$

$\implies \sf a =\: \dfrac{\cancel{63}}{\cancel{7}}$

$\implies \sf\bold{\red{a =\: 9}}$

Hence, the required present ages are :

✯ Present Age Of Grandson :

➳ Present Age Of Grandson = a years

➳ Present Age Of Grandson = 9 years

✯ Present Age Of Grandfather :

➳ Present Age Of Grandfather = 8a

➳ Present Age Of Grandfather = 8(9)

➳ Present Age Of Grandfather = 8 × 9

➳ Present Age Of Grandfather = 72 years

$\therefore$ The present age of grandfather is 72 years and the present age of grandson is 9 years .

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VERIFICATION :-

$\leadsto \bf a + 63 =\: 8a$

By putting a = 9 we get,

$\leadsto \sf 9 + 63 =\: 8(9)$

$\leadsto \sf\bold{\purple{72 =\: 72}}$

$\leadsto \sf\bold{\green{L.H.S =\: R.H.S}}$

Hence Verified !