CDS 2026 (I) Elementary Mathematics, question 20

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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Q20

The ratio of the present age of X to that of Y is 4:54:5. kk (less than 1010) years ago, this ratio was 1:21:2. How many values of kk are possible if the ages are expressed in complete years ?

  1. (a) 11
  2. (b) 22
  3. (c) 33Correct answer
  4. (d) More than 3

Solution.

Answer: (c) 33

  1. Write the present whole-number ages as 4t and 5t, where t is a positive integer.
  2. The past ratio gives (4t−k)/(5t−k)=1/2(4t - k)/(5t - k) = 1/2, so k=3tk = 3t.
  3. Since 0<k<10,k0 < k < 10,k can be 3, 6 or 9.
  4. The corresponding past ages are t and 2t, so all three cases are valid.