Question

2women and 5 men can together finish a work in 5 days while 3 women and 6 men can finish it in 3 days find the time taken by one women alone to finish the work and also that taken by one man alone​

Answer 1

Answer:

Suppose that

1 women alone can finish the work in X days and

1 man alone can finish work in Y days

Therefore,

Work done by 1 women in 1 day = 1/x

Work done by 1 men in 1 day = 1/y

Then, work done by 2 women & 5 men together in 1 day = ( 2/x + 5/y).

But aaccording to first information given, 2 women and 5 men together finish the work in 4 days.that is in one day they can finish 1/4 part of the work.

Hence,we get the following equation:

2/x + 5/y = 1/4 ........(1)

Similarly from the second information given we get,

3/x + 6/y = 1/3 .........(2)

Taking 1/x = a and 1/y = b in both the equations we get,

2a + 5b = 1/4 ........(3)

3a + 6b = 1/3 .........(4)

Multiply equation (3)by 6 and equation (4) by 5 we get ,

12a + 30b = 6/4 ......(5)

15a + 30b = 5/3 .......(6)

subtracting equation (5) from equation (6) we get,

(15a + 30b) - (12a + 30b) = 5/3 - 6/4

15a + 30b - 12a - 30b = 20 - 18/ 12

3a = 2/12

a = 1/18

Substituting a = 1/3 in equation ( 3),

we get,

2 (1/18) + 5b = 1/4

5b = 1/4 - 1/9

5b = 5/36

b = 1/36

Now a = 1/x = 1/18 Therefore x = 18

and b = 1/y = 1/36 Therefore y = 36

Thus, 1 woman alone can finish the work in 18 days and 1 man can finish the work in 36 days.

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