Question

10 women and 20 gilts can finish a piece of work in 2 days, while 6 women and 4 girls can finish it in 5 days. Find the taken by 1 women alone and that by 1 girl alone to finish the work...
Plz answer this question,,,,,,,

Answer 1

$\huge\underbrace\mathfrak \red{ANSWER }$

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}x1

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}y1

According to question

\frac{10}{x}+\frac{20}{y}=\frac{1}{2}x10+y20=21 ..(1)

\frac{6}{x}+\frac{4}{y}=\frac{1}{5}x6+y4=51 ...(2)

Substitute \frac{1}{x}=u,\frac{1}{y}=vx1=u,y1=v

10u+20v=\frac{1}{2}10u+20v=21

20u+40v=120u+40v=1 ..(3)

6u+4v=\frac{1}{5}6u+4v=51

30u+20v=130u+20v=1 ...(4)

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

-40u=-1−40u=−1

u=\frac{-1}{-40}=\frac{1}{40}u=−40−1=401

Substitute the value of u in equation (3)

20\times \frac{1}{40}+40v=120×401+40v=1

\frac{1}{2}+40v=121+40v=1

40v=1-\frac{1}{2}=\frac{1}{2}40v=1−21=21

v=\frac{1}{2\times 40}=\frac{1}{80}v=2×401=801

u=\frac{1}{x}u=x1

\frac{1}{40}=\frac{1}{x}401=x1

x=40x=40

v=\frac{1}{y}v=y1

\frac{1}{80}=\frac{1}{y}801=y1

y=80y=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

HOPE SO IT WILL HELP....