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Question

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.  [4 MARKS]


Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Let the work completed by 1 man in a day  be m

& that by a woman be w

Then, 1 man's 1 day's work =1m

Then, 1 woman's 1 day's work =1w

2 women and 5 men can together finish an embroidery work in 4 days

2w+5m=14

2x+5y=14(i)  where 1w=x,1m=y

Similarly,

3w+6m=13

3x+6y=13(ii) where 1w=x,1m=y

Solving (i) and (ii) we get,

 2x=145y

x=120y8

Substituting value of x in (ii)

3x+6y=13

3(120y8)+6y=13

360y+48y8=13

y=136 

Now,  x=120y8

x=120(136)8

x=118

y=136

1m=136m=36

one man alone can complete the wok in 36 days

x=118

1w=118w=18

one woman alone can complete the wok in 18 days

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