Question

Q2. The ages of A & B are in the ratio
2:5. After 6 years their ages will be in
the ratio 1:2. Find the present age of
B. (2)
O A. 30 yrs
O B. 33 yrs
O C. 35 yrs​

Answer 1

Answer :-

30 years [ option A. ] is correct.

Step-by-step explanation:-

To Find :-

• The present age of B .....(?)

Solution :-

Let the A be 2x and B be 6x.

Given that,

$\purple \longrightarrow \tt{ \dfrac{2x + 6}{5x + 6} = \dfrac{1}{2}}$

Now, Simplification :

$\purple \longrightarrow \tt{ \dfrac{2x + 6}{5x + 6} = \dfrac{1}{2}}$

Simplifying the values with cross multipcation

$\purple \longrightarrow \tt{2(2x + 6) = 1(5x + 6)}$

$\purple \longrightarrow \tt{4x + 12 = 5x + 6}$

$\purple \longrightarrow \tt{4x - 5x = 6 - 12}$

$\purple \longrightarrow \tt{ - x = - 6}$

$\purple \longrightarrow \tt{x = 6}$

Therefore, value of x is 6

Now, Let's find their ages :

$\tt{Given, \: A's \: \: age = 2x}$

$\purple \longrightarrow \tt{2 \times 6}$

$\purple \longrightarrow \tt{12 \: \: years}$

$\tt{Given, \: \: B's \: \: age = 5x}$

$\purple \longrightarrow \tt{5 \times 6}$

$\longrightarrow \sf{30 \: \: years} \: \: \orange{ \star}$

$\boxed{ \underline{ \sf{B's\: \: age \: \: is \: \: 30 \: \: years}}}$