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A, B, and C can do a piece of work in 15 days, 18 days, and 24 days respectively. They started work together, but after 5 days A left the work, B left the work 6 days before the completion of the work. In how many days the work gets completed?1. \(10\frac{2}{7}\)2. \(10\frac{6}{7}\)3. \(8\frac{4}{5}\)4. \(11\frac{2}{7}\) |
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Answer» Correct Answer - Option 1 : \(10\frac{2}{7}\) Given: A can do a piece of work = 15 days B can do a piece of work = 18 days C can do a piece of work = 24 days Calculations: Let the total work done be in 'x' days A's one day's work = 1/15 A worked for 5 days = 1/3 A can do 1/3 of work in 5 days B's one day work = 1/18 B's (x - 6) days work = (x - 6)/18 C's one day work = 1/24 C's 'x' days work = x/24 (A + B + C) together work = 1 ⇒ 1/3 + (x - 6)/18 + x/24 = 1 ⇒ (24 + 4x - 24 + 3x)/72 = 1 ⇒ 7x = 72 ⇒ x = 72/7 ⇒ x = \(10\frac{2}{7}\) ∴ The number of days together is \(10\frac{2}{7}\) days |
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