Question

10 women and 20girls can finish a piece of work in 2 days, while 6 women and 4 girls can finish it in 5 days. find the time taken by 1 women alone and that by 1 girl alone to finish the work ​

Answer 1

Answer:

12

Step-by-step explanation:

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Answer 2

Time taken by 1 women alone to finish the work=40 days

Time taken by 1 girls alone to finish the work=80 days

Step-by-step explanation:

Let 1 women takes time to finish 1 work=x days

In x days work can finished by 1 women=1

In 1 day work can finished by 1 women=$\frac{1}{x}$

1 girl takes time to finish work=y days

In y days work can finished   by 1 girl=1

In 1 day work can finished by 1 girl=$\frac{1}{y}$

According to question

$\frac{10}{x}+\frac{20}{y}=\frac{1}{2}$..(1)

$\frac{6}{x}+\frac{4}{y}=\frac{1}{5}$...(2)

Substitute $\frac{1}{x}=u,\frac{1}{y}=v$

$10u+20v=\frac{1}{2}$

$20u+40v=1$..(3)

$6u+4v=\frac{1}{5}$

$30u+20v=1$...(4)

Equation (4) multiply by and then subtract from equation (3)

$-40u=-1$

$u=\frac{-1}{-40}=\frac{1}{40}$

Substitute the value of u in equation (3)

$20\times \frac{1}{40}+40v=1$

$\frac{1}{2}+40v=1$

$40v=1-\frac{1}{2}=\frac{1}{2}$

$v=\frac{1}{2\times 40}=\frac{1}{80}$

$u=\frac{1}{x}$

$\frac{1}{40}=\frac{1}{x}$

$x=40$

$v=\frac{1}{y}$

$\frac{1}{80}=\frac{1}{y}$

$y=80$

Hence, Time taken by 1 women alone to finish the work=40 days

Time taken by 1 girl alone to finish the work=80 days

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