Question
If X and Y complete a certain work in 10 days, Y and Z in 16 days and X and Z in 22 days, find the time required for each one to complete the work while working separately.
Answer: Option A
LET A: BE THE TIME IN WHICH X & Y COMPLETES THEIR WORK = 30 DAYS
B: TIME IN WHICH Y & Z COMPLETES THEIR WORK = 24 DAYS
C: TIME IN WHICH X & Z COMPLETES THEIR WORK = 40 DAYS
X ALONE CAN COMPLETE THE WORK IN (2 * A * C) / (AB + BC – AC) DAYS
= 2 * 30 * 24 * 40 / ((30 * 24) + (24 * 40) – (30 * 40)) = 120 DAYS
Y ALONE CAN COMPLETE THE WORK IN 2 * A * B * C / (- AB + BC + AC) DAYS
= 2 * 30 * 24 * 40 / (-(30 * 24) + (24 * 40) + (30 * 40)) = 40 DAYS
Z ALONE CAN COMPLETE THE WORK IN 2 * A * B * C / (AB – BC + AC) DAYS
= 2 * 30 * 24 * 40 / ((30 * 24) – (24 * 40) + (30 * 40))
= 60 DAYS
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LET A: BE THE TIME IN WHICH X & Y COMPLETES THEIR WORK = 30 DAYS
B: TIME IN WHICH Y & Z COMPLETES THEIR WORK = 24 DAYS
C: TIME IN WHICH X & Z COMPLETES THEIR WORK = 40 DAYS
X ALONE CAN COMPLETE THE WORK IN (2 * A * C) / (AB + BC – AC) DAYS
= 2 * 30 * 24 * 40 / ((30 * 24) + (24 * 40) – (30 * 40)) = 120 DAYS
Y ALONE CAN COMPLETE THE WORK IN 2 * A * B * C / (- AB + BC + AC) DAYS
= 2 * 30 * 24 * 40 / (-(30 * 24) + (24 * 40) + (30 * 40)) = 40 DAYS
Z ALONE CAN COMPLETE THE WORK IN 2 * A * B * C / (AB – BC + AC) DAYS
= 2 * 30 * 24 * 40 / ((30 * 24) – (24 * 40) + (30 * 40))
= 60 DAYS
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