Four years ago, the ratio of half the age of A to 1/3 of the age of B

1.	Four years ago, the ratio of half the age of A to 1/3 of the age of B is 8 ∶ 7. Also half of the present age of B exceeds 1/3 of present age of A by 11. Find the present age of A?1. 462. 363. 664. 565. 48
Answer» Correct Answer - Option 2 : 36 Given: Four years ago, the ratio of half the age of A to 1/3 of the age of B = 8 ∶ 7 Half of the present age of B exceeds 1/3 of present age of A by 11 Calculations: Let the present ages of A and B be a and b respectively. Four years ago A’s age = (a – 4) Four years ago B’s age = (b – 4) Four years ago, the ratio of half the age of A to 1/3 of the age of B = 8 ∶ 7 \( \Rightarrow \;\frac{{\frac{1}{2}\; \times\; \left( {a\; - \;4} \right)}}{{\frac{1}{3}\; \times\; \left( {b\; - \;4} \right)}} = \frac{8}{7}\) ⇒ 21a – 16b = 20 ----(1) Half the present age of B exceeds 1/3 of present age of A by 11 ⇒ b/2 = a/3 + 11 ⇒ 2a – 3b = -66 ----(2) On solving equation (1) and (2) ⇒ a = 36 year and b = 46 years ∴ The present age of A is 36

Four years ago, the ratio of half the age of A to 1/3 of the age of B is 8 ∶ 7. Also half of the present age of B exceeds 1/3 of present age of A by 11. Find the present age of A?1. 462. 363. 664. 565. 48

Answer» Correct Answer - Option 2 : 36

Given:

Four years ago, the ratio of half the age of A to 1/3 of the age of B = 8 ∶ 7

Half of the present age of B exceeds 1/3 of present age of A by 11

Calculations:

Let the present ages of A and B be a and b respectively.

Four years ago A’s age = (a – 4)

Four years ago B’s age = (b – 4)

Four years ago, the ratio of half the age of A to 1/3 of the age of B = 8 ∶ 7

\( \Rightarrow \;\frac{{\frac{1}{2}\; \times\; \left( {a\; - \;4} \right)}}{{\frac{1}{3}\; \times\; \left( {b\; - \;4} \right)}} = \frac{8}{7}\)

⇒ 21a – 16b = 20 ----(1)

Half the present age of B exceeds 1/3 of present age of A by 11

⇒ b/2 = a/3 + 11

⇒ 2a – 3b = -66 ----(2)

On solving equation (1) and (2)

⇒ a = 36 year and b = 46 years

∴ The present age of A is 36