Multiple choice

A alone complete the work in x days and B alone complete the work in (x + 32) days. If A and B started the work together, after 6 days they complete the 20% of the work, in how many days A alone complete the work? A अकेले कार्य को x दिनों में पूरा करता है और B अकेले कार्य को (x + 32) दिनों में पूरा करता है। यदि A और B एक साथ काम शुरू करते हैं, तो 6 दिनों के बाद वे काम का 20% पूरा करते हैं, A अकेले उस काम को कितने दिनों में पूरा करेगा?

  1. 44 days 44 दिन

  2. 45 days 45 दिन

  3. 42 days 42 दिन

  4. 48 days 48 दिन

  5. 50 days 50 दिन
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D Correct answer
Explanation

Let total work = 1 unit. A's rate = 1/x and B's rate = 1/(x+32). Together their rate = 1/x + 1/(x+32). In 6 days they complete 20% (0.2) of work: 6(1/x + 1/(x+32)) = 0.2. Solving: 6(x+32 + x)/x(x+32) = 0.2, so 12x + 192 = 0.2x² + 6.4x. Rearranging: 0.2x² - 5.6x - 192 = 0, or x² - 28x - 960 = 0. Using quadratic formula: x = [28 ± √(784 + 3840)]/2 = [28 ± √4624]/2 = [28 ± 68]/2. So x = 48 (positive root). A alone takes 48 days.

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