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X and Y can finish a work in 9 and 8 days respectively. X works for 4 days and then left. Y works for another 3 days and then left and then Z joined and finished the remaining work in 1 day. Find the time X and Z would take to finish the same work.1. 24/72. 29/73. 32/74. 26/7 |
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Answer» Correct Answer - Option 1 : 24/7 Given: X and Y can finish a work in 9 and 8 days respectively. X works for 4 days and then left. Y works for another 3 days and left. Then Z joined and finished the remaining work in 1 day. Formula Used: If A and B can together finish a work in t days and alone can finish the work in a and b days respectively, Then, 1/a + 1/b = 1/t Work = Time × Efficiency Calculation: LCM of 9, 8 = 72 Efficiency of X = 8 units Efficiency of Y = 9 units Work done by X in 4 days = 8 × 4 = 32 Work done by Y in 3 days = 3 × 9 = 27 Remaining work = 72 – 32 – 27 = 13 Z finished the remaining work in 1 day. Efficiency of Z = 13 units Time X and Z would take = total work/efficiency of X + Z = 72/(13 + 8) = 72/21 = 24/7 days ∴ Required time is 24/7 days. |
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