CDS 2026 (I) Elementary Mathematics, question 35

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

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Q35

Two numbers P and Q are such that P:Q=x:yP:Q=x:y. If 11 is added to both the numbers, the ratio becomes 7:107:10. If 33 is added to both the numbers, the ratio becomes 3:43:4. What is (x+y):(x−y)(x+y):(x-y) equal to ?

  1. (a) −5-5Correct answer
  2. (b) −3-3
  3. (c) 33
  4. (d) Cannot be determined due to insufficient data

Solution.

Answer: (a) −5-5

  1. The two ratios give 10P−7Q=−310P - 7Q = - 3 and 4P−3Q=−34P - 3Q = - 3.
  2. Solving yields P=6P = 6 and Q=9Q = 9, so x:y=2:3x:y = 2:3.
  3. Therefore (x+y)/(x−y)=(2+3)/(2−3)=−5(x + y)/(x - y) = (2 + 3)/(2 - 3) = - 5.