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Question

2 women and 5 men together finish an embroidery work in 4 days while 3 women and 6 men can together finish within 3days .Find the time taken by 1 women alone to finish the work and also 1 men to finish.

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Solution

Let w and m represent women and men respectively

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

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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