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4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women finish it?

Solution

✅ Correct Option: 4

Let's say one man's work per day = MM units

One woman's work per day = WW units

Total work = TT units

From first equation:

(4M+6W)×8=T(4M + 6W) × 8 = T --> Eq. 1

From second equation:

(3M+7W)×10=T(3M + 7W) × 10 = T --> Eq. 2

Equating (1) and (2):

32M+48W=30M+70W32M + 48W = 30M + 70W

32M−30M=70W−48W32M - 30M = 70W - 48W

2M=22W2M = 22W

M=11WM = 11W

Substituting back in equation (1):

(44W+6W)×8=T(44W + 6W) × 8 = T

50W×8=T50W × 8 = T

400W=T400W = T

For 10 women to do total work TT:

10W×t=400W10W × t = 400W

t=40t = 40

Therefore, 10 women will finish the job in 40 days.

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