Question
Download Solution PDF25 men and 45 women can complete a piece of work in 15 days, while 15 men and 60 women can complete it in 20 days. In how many days can 69 men and 67 women complete the work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
25 men and 45 women complete work in 15 days
15 men and 60 woman complete the work in 20 days
Formula Used:
M1D1 = M2D2
Calculations:
As in both case they complete the same work
so,
⇒ M1D1 = M2D2
⇒
⇒
⇒ 75M + 135W = 60M + 240W
⇒ 75M - 60M = 240W -135W
⇒ 15M = 105W
⇒
⇒
⇒ Efficiency of Men = 7
⇒ Efficiency of Woman = 1
⇒ Total efficiency of men and woman = 25M + 45W = 25 × 7 + 45 × 1 = 175 + 45 = 220
⇒ Total work = Efficiency × Time = 220 × 15 = 3300
Now, the Efficiency of 69 men and 67 women
⇒ Efficiency = 69 × 7 + 67 × 1 = 483 + 67 = 550
Time is taken by 69 men and 67 women to complete the work
⇒ Time = Total work / Efficiency = 3300 / 550 = 6 days
⇒ Hence, The time taken by 69 men and 67 women is 6 days
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