If 5 men and 7 women can plough a field in 10 days while 20 men and 42 women do the same work in 2 d...........

Quant (SSC) Time and work

If 5 men and 7 women can plough a field in 10 days while 20 men and 42 women do the same work in 2 days, find the time taken by 10 men and 15 women to plough the field.

5 days

5 24/29 days

6 days

4 24/29 days

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Explanation:

(5m + 7w) × 10 = (20m + 42w) × 2
⇒ 50m + 70w = 40m + 84w
⇒ 10m = 14w
⇒ 5m = 7w
Or, 1m = 7/5w
Now, (5m + 7w)
= 5 × 7/5w + 7w = 14 w
Similary, (10m + 15w)
= 10 × 7/5x + 15w = 29w
Now, apply the chain rule method,
M₁D₁ = M₂D₂
M₁ = 14, M₂ = 29w, D₁ = 10 days, D₂ = ?
14 × 10 = 29 × ?
? = 140/29 days = 4 24/29 days