Question

the age of a is 1/3 of the age of b . After 15 years , the age of a will be half of the age of b. Find their present age​

Answer 1

༒ Let :-

Present age of a be = x years.

Present age of b be = y years

___________________________

༒ Given :-

▪The age of a is 1/3 of age of b

and

After 15 years

▪The age of a will be half of the age of b.

___________________________

༒ Solution :-

According to the Given Condition,

$\sf x = \frac{y}{3} \\ \\ \implies \underline{\boxed{ \bf y = 3x}} \: \: \: . \: . \: . \: \{ \bf i \}$

After 15 years,

Age of a will be = x + 15

Age of b will be = y+ 15

According to the Given Condition,

$\bf x + 15 = \dfrac{y + 15}{2} \: \: \: \: . \: .\: .\: \{i i\}$

Putting {i} in {ii} we get,

$\sf x + 15 = \frac {3x + 15}{2} \\ \\ \implies \sf 2x + 30 = 3x + 15 \\ \\ \implies \Large \bf \underline{ \boxed{\bf x = 15 \: years}}$

Putting Value of x in eq {i} we get

$\Large\bf\underline{ \boxed{\bf y = 45 \: years}}$

So,

Present age of a = 15 years

And

Presentage of b = 45 years.

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required }}\\ \huge \red{ \mathfrak{ \text{ A}nswer.}}$

Answer 2

Given :-

The age of a is 1/3 of the age of b . After 15 years , the age of a will be half of the age of b

To Find :-

Present age

Solution :-

Age of a = 1/3 × b

After 15 years

Age of a = a + 15

Age of b = b + 15

Now

a + 15 = b + 15/2

b/3 + 15 = b + 15/2

b + 45/3 = b + 15/2

3(b + 15) = 2(b + 45)

3b + 45 = 2b + 90

3b - 2b = 90 - 45

b = 45

Age of a = 1/3 × 45

Age of a = 15 years