Question : 25 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?
Option 1: 10
Option 2: 5
Option 3: 8
Option 4: 6
Correct Answer: 6
Solution :
According to the question, they complete the same work
⇒ M
1
D
1
= M
2
D
2
⇒ (25M + 45W) × 15 = (15M + 60W) × 20
⇒ (25M + 45W) × 3 = (15M + 60W) × 4
⇒ 75M + 135W = 60M + 240W
⇒ 75M – 60M = 240W – 135W
⇒ 15M = 105W
⇒ $\frac{\text{M}}{\text{W}}=\frac{7}{1}$
Let the efficiency of Men = 7 and the efficiency of Women = 1
⇒ Total efficiency of 25 men and 45 women = 25M + 45W = 25 × 7 + 45 × 1 = 175 + 45 = 220
Now, Total work = Efficiency × Time = 220 × 15 = 3300
And, The Efficiency of 69 men and 67 women
⇒ 69 × 7 + 67 × 1 = 483 + 67 = 550
$\therefore$ The time is taken by 69 men and 67 women to complete the work = $\frac{\text{Total work}}{\text{Efficiency}} = \frac{3300}{550} = 6$ days
Hence, the correct answer is 6.
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