Multiple choice

Nine years ago, the age of a father was three years more than six time the age of his son. Four years hence, his age will be seven years less than 3.5 times the age of his son. After how many years from now will their combined age be 100 years? नौ वर्ष पहले एक पिता की उम्र अपने बेटे की उम्र के छह गुने से तीन वर्ष अधिक थी । चार वर्ष पश्चात उसकी उम्र उनके बेटे की उम्र के 3.5 गुना से सात वर्ष कम होगी। अब से कितने वर्षों के बाद उनकी संयुक्त उम्र 100 वर्ष हो जाएगी?

  1. 2

  2. 8

  3. 12

  4. 9

  5. None of these इनमें से कोई नहीं
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B Correct answer
Explanation

Let father's current age = f, son's current age = s. Nine years ago: (f-9) = 6(s-9) + 3, giving f - 9 = 6s - 54 + 3 or f = 6s - 42. Four years hence: (f+4) = 3.5(s+4) - 7, giving f + 4 = 3.5s + 14 - 7 or f = 3.5s + 3. Solving: 6s - 42 = 3.5s + 3, giving 2.5s = 45 or s = 18. Father's age f = 6×18 - 42 = 66. Current sum = 84. We need sum to be 100, which is 16 more. In x years, sum = 84 + 2x = 100, giving 2x = 16 or x = 8.

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