Question

Kavitha thought of constructing 2 more rooms in her house. She enquired about the labour. She came to know that 6 men and 8 women could finish this work in 14 days. But she wanted the work completed in only 10 days. When she enquired, she was told that 8 men and 12 women could finish the work in 10 days. Find out that how much time would be taken to finish the work if one man or one woman worked alone?

Answer 1

Hi ,

Let one men alone can finish the work

in ' x ' days

And

One women alone can finish the work

in ' y ' days .

Part of work done by the men in

one day = 1/x

Part of work done by the women

in one day = 1/y

Given ,

6 men and 8 women can finish the

work in 14 days

6/x + 8/y = 1/14

14 ( 6/x + 8/y ) = 1

84/x + 112/y = 1 --( 1 )

8 men and 12 women can finish the

work in 10 days

8/x + 12/y = 1/10

10( 8/x + 12/y ) = 1

80/x + 120/y = 1 ---( 2 )

Let 1/x = a and 1/y = b in equation ( 1 ) and

( 2 ) , then

84a + 112b = 1 -----( 3 )

80a + 120b = 1------( 4 )

multiply ( 3 ) with 20 and ( 4 ) with 21

we get

1680a + 2240b = 20---( 5 )

1680a + 2520b = 21 ----( 6 )

subtract ( 5 ) from ( 6 ) , we get

280b = 1

b = 1/280

Put b = 1/280 in ( 4 ) , we get

a = 1/140

Therefore ,

a = 1/140 = 1/x => = x = 140,

b = 1/280 = 1/y => y = 280

A man alone can finish work in 140 days

and

A women alone can finish the work in

280 days

I hope this helps you.

: )

Answer 2

Answer:

it's a sum in 'pair of linear equations'

Step-by-step explanation:

see above 5 pictures