Multiple choice

The ratio of the earnings of A and $\mathrm { B }$ is $ 4: 7 .$ If the earnings A increase by 50$\%$ and those of B decrease by 25$\% $, the new ratio of their earnings becomes $ 8: 7 .$ What are A's earnings?

  1. Rs. $21,000$
  2. Rs. $26,000$
  3. $\mathrm { Rs } .28,000$

  4. Data inadequate
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let earnings be 4x and 7x. New earnings are 4x * 1.5 = 6x and 7x * 0.75 = 5.25x. The ratio 6x / 5.25x = 6 / 5.25 = 600 / 525 = 8/7. Since the ratio is satisfied for any x, the actual earnings cannot be determined without a specific total or value.

AI explanation

Let the initial earnings of A and B be 4x and 7x respectively. After a 50 percent increase, A's new earning is 6x; after a 25 percent decrease, B's new earning is 5.25x. The new ratio becomes 6x to 5.25x, which simplifies to 8 to 7. Since this holds true for any value of x, a unique numerical value for the earnings cannot be determined. Therefore, the data is inadequate.

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