A is twice as old as B, ten years ago. If A was four times as old as

1.	A is twice as old as B, ten years ago. If A was four times as old as B, their present ages are ……………A) 24 and 12 B) 30 and 15 C) 32 and 16 D) 20 and 10
Answer» Correct option is (B) 30 and 15 Let A's present age be x years and B's present age be y years. Since, A is twice as old as B. \(\therefore\) x = 2y __________(1) 10 years ages, A's age = (x - 10) years & B's age = (y - 10) years Given that 10 years ago, A was four times as old as B. \(\therefore\) x - 10 = 4 (y - 10) \(\Rightarrow\) 2y - 10 = 4y - 40 (From (1)) \(\Rightarrow\) 4y - 2y = 40 - 10 \(\Rightarrow\) 2y = 30 \(\Rightarrow\) y = \(\frac{30}2\) = 15 \(\therefore\) x = 2 \(\times\) 15 = 30 (From (1)) Hence, their present ages are 30 and 15 years. Correct option is B) 30 and 15

A is twice as old as B, ten years ago. If A was four times as old as B, their present ages are ……………A) 24 and 12 B) 30 and 15 C) 32 and 16 D) 20 and 10

Answer»

Correct option is (B) 30 and 15

Let A's present age be x years and B's present age be y years.

Since, A is twice as old as B.

\(\therefore\) x = 2y __________(1)

10 years ages, A's age = (x - 10) years

& B's age = (y - 10) years

Given that 10 years ago, A was four times as old as B.

\(\therefore\) x - 10 = 4 (y - 10)

\(\Rightarrow\) 2y - 10 = 4y - 40 (From (1))

\(\Rightarrow\) 4y - 2y = 40 - 10

\(\Rightarrow\) 2y = 30

\(\Rightarrow\) y = \(\frac{30}2\) = 15

\(\therefore\) x = 2 \(\times\) 15 = 30 (From (1))

Hence, their present ages are 30 and 15 years.

Correct option is B) 30 and 15