Multiple choice

The ratio between the present ages of $P$ and $Q's$ age is $4:6$ and the ratio after $5$ Years is $5:7$, what is the sum of $P's$ and $Q's$ present ages?

  1. $48\ years$
  2. $56\ years$
  3. $50\ years$

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let present ages be 4x and 6x. After 5 years, (4x+5)/(6x+5) = 5/7. Cross-multiplying gives 28x + 35 = 30x + 25, so 2x = 10 and x = 5. The present ages are 20 and 30, so the sum is 50.

AI explanation

Let the present ages of P and Q be 4x and 6x respectively. After 5 years, the ratio equation becomes 4x plus 5 divided by 6x plus 5 equals 5 divided by 7. Cross-multiplying gives 28x plus 35 equals 30x plus 25, which simplifies to 2x equals 10, so x equals 5. The sum of their present ages is 4x plus 6x, which is 10x, resulting in 10 times 5 equaling 50 years.

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