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

Answer:

solution:-

⇨Given, ratio of age of A and B=3:1 

Let the ages of A and B be 3x and x, respectively.

Now, 15 years hence,

age of A=3x+15 and age of B=x+15. 

Then,

x+153x+15=12

⟹  3x+15=2(x+15)

⟹  3x+15=2x+30.

Transposing x terms to one side, we get,

⟹  3x−2x=30−15

⟹x=15.

∴A's age =3×15=45 years

and B's age =x=15 years.

✔Hence, it is verified

Answer 2

༒ 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,

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

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,

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

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.

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