(ii) 2 women and 5 men can together finish an
embroidery work in 4 days, while 3 women and
6 men can finish in 3 days. Find the time taken by
one woman alone to finish the work and also that
taken by one man alone.
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2W + 5M can do 1 work in 4 days
2W + 5M can do 1/4 work in 1 days
Also,
3W + 6M can do 1 work in 3days
3W + 6M can do 1/3 work in 1day
Then, equating work with men and women
2W + 5M =1/4.(i)
Then,
3W + 6M=1/3-(ii)
Or, 3(W + 2M)=1/3
Or,W + 2M =1/9-(iii)
Then subtracting (i) from (ii)
3W + 6M=1/3
-2W - 5M =-1/4)
W + M=1/3 -1/4
W + M= 1/12...............(iv)
Also,
Subtracting (iv) from (iii)
W + 2M =1/9
-W - M=-1/12
M = 1/9 – 1/12
Or, M=1/36
So subsituting m=1/36 in equation (iv)
W + 1/36 = 1/12
Or,W = 1/12 – 1/36
Hence, W=1/18
I men alone can do (1/36) work in 1 day
1 men alone can do 1 work in 36 days
Also,
1 women alone can do (1/18) in 1 day
1 women alone can do 1 work in 18 days
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