Multiple choice

Two sisters get pocket money in ratio of square roots of their ages. The elder sister is 9 years older than the younger and gets Rs. 250 more as pocket money. If the age of the elder sister had exceeded that of the younger by 4 1 4 years, then their pocket money would have been in the ratio 9 : 8. What are their respective ages?

  1. 17 years and 8 years

  2. 28 years and 19 years

  3. 25 years and 16 years

  4. 47 years and 38 years

  5. 42 years and 30 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the younger sister be y years old. The second condition gives sqrt((y+4.25)/y) = 9/8, so (y+4.25)/y = 81/64, yielding y = 16. The elder sister is then 16+9 = 25 years old, confirming option C.

AI explanation

Let the pocket money ratio be the square root of their ages, and test the given options. For the ages 25 years and 16 years, the difference in age is 9 years, and the difference in pocket money is sqrt(25) - sqrt(16) = 5 - 4 = 1 unit, meaning 1 unit equals Rs. 250. If the age difference were 4.25 years instead, the ratio of pocket money would be 9 : 8, which aligns with the hypothetical condition. Therefore, their respective ages are 25 years and 16 years.

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