Question

Present age of grandfather is ten times that of his granddaughter. He is also $54$ years older than her. Find their present ages.

• A. Grand daughters age: $7$ years; Grandfathers age: $40$ years
• B. Grand daughters age: $6$ years; Grandfathers age: $60$ years
• C. Grand daughters age: $8$ years; Grandfathers age: $50$ years
• D. Grand daughters age: $5$ years; Grandfathers age: $30$ years

Answer 1

Answer: (B)

Grand daughters age: $6$ years; Grandfathers age: $60$ years

Let the Granddaughter's age be $x$ and the Grandfather's age be $10x$

It is given that the grandfather is $54$ years older than her.

Therefore, $10x=54+x$

$9x=54$

$\therefore x=6$

Granddaughter's age $=6$ and Grandather's age $10x=10\times 6=60$.