Question

6 men and 10 women can finish making pots in 8 days, while the 4 men and 6 women can finish it in 12 days. Find the time taken by the one man alone from that of one woman alone to finish the work.

Answer 1

48 days

Explanation:

Let us assume the following things

Work done by 1 man in 1 day is
`(1)/(x)`

Work done by 1 woman in 1 day is
`(1)/(y)`

It is mentioned that

six men + ten women finished in 8 days

So,

`(6)/(x) + (10)/(y) = (1)/(8)` .............. (1)

And,

four men + six women finished in 12 days

`(4)/(x) + (6)/(y) = (1)/(12)` ...............(2)

Now solve these two equations

And we assume
`(1)/(x)` be u and
`(1)/(y)` be v

So

Now the equation is

`6u\ + 10v\ = (1)/(8) \\\\\4u\ + 6v\ = (1)/(12)`

So,

u = 1 ÷ 48 , v = 0

Therefore x = 48

So the time taken for finish the work is 48 days