Question

A father's age is 4 times his daughters age. The sum of their age is 60 years. find their present age​

Answer 1

$\mathfrak{ \large{ \orange{ \underline{ \pink{Correct \: Question: }}}}}$

A father's age is 4 times his daughters age. The sum of their age is 60 years. find their present age

$\mathfrak{ \large{ \orange{ \underline{ \pink{Given: }}}}}$

• Sum of ages of father and daughter = 60
• Father's age is 4 times the age of daughter

$\mathfrak{ \large{ \orange{ \underline{ \pink{To\: Find:}}}}}$

• Present age of daughter and father

$\mathfrak{ \large{ \orange{ \underline{ \pink{Solution: }}}}}$

• Let the age of daughter be x
• Let the age of father be 4x

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \: 4x + x = 60}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \: 5x = 60}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \: x = \cancel \frac{60}{5} }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ \mathfrak{ \green{ x = 12}}}} }{ \large{\star}}$

Now,

• The age of daughter = x = 12 years
• The age of father = 4x = 48 years

$\mathfrak{ \large{ \orange{ \underline{ \pink{ Hence:}}}}}$

The age of daughter and father are 12 years and 48 years.

Answer 2

Y = Father's present age, x = daughters age, father is 4 times older so

Y = 4x

In 4 years fathers age = Y+4 and will be 3 times daughters age which is

Daughters age will be x + 4 so

Y + 4 = 3(x + 4)

Y+4= 3x+12 isolate Y by subtracting 4 from each side so

Y+4–4 = 3x +12 -4

Y = 3X +8

Y from present age = 4x

So

4x = 3x +8

4× -3× = 3x +8 - 3x

X = 8

Father's present age = 4x = 4× 8= 32

In four years father will be 32+4=36

Daughter will be x+4 = 8+4 = 12

36 is 3(x +4) = 3 × (8+4) = 3 × 12

Hope it helps you ...