CDS 2026 (I) Elementary Mathematics, question 11

Topic: Algebra

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Q11

Seven times a two-digit positive number is equal to four times the number obtained by reversing the order of the digits. How many such two-digit numbers are there ?

  1. (a) 11
  2. (b) 44Correct answer
  3. (c) 66
  4. (d) 88

Solution.

Answer: (b) 44

  1. Let the number be 10a+b10a + b, where a is its nonzero tens digit.
  2. Then 7(10a+b)=4(10b+a)7(10a + b) = 4(10b + a), giving 66a=33b66a = 33b and hence b=2ab = 2a.
  3. The digit restriction b≤9b \leq 9 allows a=1,2,3,4a = 1,2,3,4.
  4. The numbers are 12, 24, 36 and 48.