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Mathematics

The ages of A and B are in the ratio 2 : 5. After 6 years, their ages will be in the ratio 1 : 2. The present age of B is

  1. 20 years
  2. 24 years
  3. 30 years
  4. 36 years

Linear Eqns One Variable

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Answer

The ages of A and B are in the ratio 2 : 5.

Let the present age of A be 2x years.

Let the present age of B be 5x years.

After 6 years:

Age of A = (2x + 6) years.

Age of B = (5x + 6) years.

The problem states that after 6 years, their ages will be in the ratio 1 : 2.

∴2x+65x+6=12⇒2(2x+6)=1(5x+6)[By cross multiplication]⇒4x+12=5x+6⇒4x−5x=6−12[Transposing +12 to RHS and +5x to LHS]⇒−x=−6⇒x=6\therefore \dfrac{2x + 6}{5x + 6} = \dfrac{1}{2} \\[1em] \Rightarrow 2(2x + 6) = 1(5x + 6) \quad \text{[By cross multiplication]} \\[1em] \Rightarrow 4x + 12 = 5x + 6 \\[1em] \Rightarrow 4x - 5x = 6 - 12 \quad \text{[Transposing +12 to RHS and +5x to LHS]} \\[1em] \Rightarrow -x = -6 \\[1em] \Rightarrow x = 6

Present age of A = 2x = 2(6) = 12 years.

Present age of B = 5x = 5(6) = 30 years.

∴ The present age of B is 30 years.

Hence, option 3 is the correct option.

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