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X can complete 5/7 part of a work in 10 days and Y can complete 3/4 part of the same work in 9 days. In how many days will both complete 13/21 part of the total work
- A6
- B4
- C3
- D12
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CCommunity
Time taken by X to complete 5/7 part of a work = 10 days
Time taken by X to complete the whole work = 10 × 7/5 = 14 days
Time taken by Y to complete 3/4 part of a work = 9 days
Time taken by Y to complete the whole work = 9 × 4/3 = 12 days
Total work = LCM of (12 and 14) = 84 units
Efficiency of X = 84/12 = 7 units/day
Efficiency of Y = 84/14 = 6 units/day
Efficiency of X + Y together = 7 + 6 = 13 units/day
∴ Total time taken by X + Y together to complete 13/21 part of the work = 84 × 13/21 × 1/13 = 4 days
Time taken by X to complete the whole work = 10 × 7/5 = 14 days
Time taken by Y to complete 3/4 part of a work = 9 days
Time taken by Y to complete the whole work = 9 × 4/3 = 12 days
Total work = LCM of (12 and 14) = 84 units
Efficiency of X = 84/12 = 7 units/day
Efficiency of Y = 84/14 = 6 units/day
Efficiency of X + Y together = 7 + 6 = 13 units/day
∴ Total time taken by X + Y together to complete 13/21 part of the work = 84 × 13/21 × 1/13 = 4 days