Multiple choice

2 years ago, mother’s age was four times the son’s age. After 6 years, mother’s age is 10 years more than twice the son’s age. What is the ratio of their ages ?

  1. 37 : 12

  2. 38 : 11

  3. 12 : 37

  4. 11 : 32

  5. 11 : 38
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B Correct answer
Explanation

Let mother's current age be M and son's current age be S. 2 years ago: M-2 = 4(S-2). After 6 years: M+6 = 2(S+6) + 10. Solving: M-2 = 4S-8 gives M = 4S-6. Substituting in second equation: 4S-6+6 = 2S+12+10, so 4S = 2S+22, giving 2S = 22 or S = 11. Then M = 4(11)-6 = 38. Current ratio M:S = 38:11.

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