Multiple choice

Ten years ago, the age of a man was 20 years less than 6 times his son's age. Ten years hence, his age will be 30 years less than thrice his son's age. After how many years from now will their combined age be 90 years? दस वर्ष पहले, एक आदमी की उम्र उसके बेटे की उम्र के 6 गुना से 20 वर्ष कम थी। दस वर्ष बाद, उसकी उम्र उसके बेटे की उम्र के तीन गुने से 30 वर्ष कम होगी। अब से कितने वर्ष बाद उनकी संयुक्त आयु 90 वर्ष होगी?

  1. 5

  2. 10

  3. 15

  4. 20

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let man's present age = M, son's present age = S. Ten years ago: M-10 = 6(S-10) - 20. Ten years hence: M+10 = 3(S+10) - 30. Solving: From first eq, M = 6S - 60 - 20 + 10 = 6S - 70. Substituting in second: 6S - 70 + 10 = 3S + 30 - 30, giving 6S - 60 = 3S, so 3S = 60, S = 20. Then M = 6(20) - 70 = 50. Current sum = 70. Sum reaches 90 in (90-70)/(1+1) = 10 years.