Question : 4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can complete it in 10 days. To complete the same work in 7 days, how many women should assist 4 men?
Option 1: 13
Option 2: 14
Option 3: 15
Option 4: 11
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Correct Answer: 13
Solution :
According to the question
(4 men + 5 women) × 15 = (9 men + 6 women) × 10
⇒ (4 men + 5 women) × 3 = (9 men + 6 women) × 2
⇒ 12 men + 15 women = 18 men + 12 women
⇒ 15 women – 12 women = 18 men – 12 men
⇒ 3 women = 6 men
⇒ women : men = 2 : 1
Total work = (4 men + 5 women) × 15 = (4 × 1 + 5 × 2) × 10 = (4 + 10) × 15 = 14 × 15 = 210
Let $x$ women assist 4 men to complete the work in 7 days, then
$(4 × 1 + x × 2) × 7 = 210$
⇒ $4 + 2x = 30$
⇒ $2x = 26$
⇒ $x = 13$
Hence, the correct answer is 13.
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