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

Answer:

48 days

Step-by-step explanation:

Let us assume the following things

Work done by 1 man in 1 day is $\frac{1}{x}$

Work done by 1 woman in 1 day is $\frac{1}{y}$

It is mentioned that

six men + ten women finished in 8 days

So,

$\frac{6}{x} + \frac{10}{y} = \frac{1}{8}$ .............. (1)

And,

four men + six women finished in 12 days

$\frac{4}{x} + \frac{6}{y} = \frac{1}{12}$ ...............(2)

Now solve these two equations

And we assume $\frac{1}{x}$ be u and $\frac{1}{y}$ be v

So

Now the equation is

$6u\ + 10v\ = \frac{1}{8} \\\\\4u\ + 6v\ = \frac{1}{12}$

So,

u = 1 ÷ 48 , v = 0

Therefore x = 48

So the time taken for finish the work is 48 days