Multiple choice

Two years ago a mother was 4 times as old as her son. Six years from now her age will become more than double her son’s age by 10 years. What is the present ratio of their ages? 2 वर्ष पहले माता की आयु अपने पुत्र की आयु की चार गुनी थी, अब से 6 वर्ष बाद माता की आयु अपने पुत्र की आयु की दोगुनी से 10 वर्ष ज्यादा होगी, तो उनकी वर्तमान आयु का अनुपात ज्ञात करे ?

  1. 2:1

  2. 38 : 11

  3. 19 : 7

  4. 3 : 1

  5. 0

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B Correct answer
Explanation

Let M and S be current ages. Two years ago: M-2 = 4(S-2) => M = 4S - 6. Six years from now: M+6 = 2(S+6) + 10 => M = 2S + 16. Equating: 4S - 6 = 2S + 16 => 2S = 22 => S = 11. Then M = 4(11) - 6 = 38. Ratio M:S = 38:11.

AI explanation

Two years ago, the mother was 4 times as old as her son, giving the equation M - 2 = 4(S - 2), which simplifies to M = 4S - 6. Six years from now, her age will be 10 more than double her son's age, giving M + 6 = 2(S + 6) + 10, which simplifies to M = 2S + 16. Equating the two expressions gives 4S - 6 = 2S + 16, so 2S = 22 and S = 11. The mother's present age is 38, making their ratio 38:11.