Question

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Can You Solve It;

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.​

Answer 1

Answer:

• The number of days taken by A man and woman are 36 days and 18 days respectively.

Step-by-step explanation:

Given,

• 2 women and 5 men can together finish an embroidery work in 4 days.
• 3 women and 6 men can finish it in 3 days.

To Find,

• The time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Solution,

Let's,

• The number of days taken by 1 woman be x.

And,

• The number of days taken by 1 man be y.

According To Question,

• $\tt \frac{2}{x} + \frac{5}{y} = \frac{1}{4} \: \: \: \: ...(1)$
• $\tt \frac{3}{x} + \frac{6}{y} = \frac{1}{3} \: \: \: ...(2)$

Taking,

• $\tt \frac{1}{x} = p \: \: \: and \: \: \: \frac{1}{y} = q$

Eq [1] and Eq [2] become,

$\tt 2p + 5q = \frac{1}{4} \: \: \: \\ \\ \tt 8p + 20q - 1 = 0 \: \: \: ...(3) \\ \\ \tt 3p + 6q = \frac{1}{3} \\ \\ \tt 9p + 18q - 1= 0 \: \: \: ...(4)$

By Cross Multiplication method,

$:\implies\tt \frac{p}{ - 20 - ( - 18)} = \frac{q}{ - 9 - ( - 8)} = \frac{1}{144 - 180} \\ \\ :\implies\tt \frac{p}{ - 20 + 18} = \frac{q}{ - 9 + 8} = \frac{1}{ - 36} \\ \\ :\implies\tt \frac{p}{ - 2} = \frac{q}{ - 1} = \frac{1}{ - 36} \\ \\ :\implies\tt \frac{p}{ - 2} = \frac{1}{ - 36} \: \: \: and \: \: \: - q = \frac{1}{ - 36} \\ \\ :\implies\tt p = \frac{1}{18} \: \: \: and \: \: \: q = \frac{1}{36} \\ \\ :\implies\tt p = \frac{1}{x} \: \: \: and \: \: \: q = \frac{1}{y} \\ \\ :\implies\tt \frac{1}{x} = \frac{1}{18} \: \: \: and \: \: \: \frac{1}{y} = \frac{1}{36} \\ \\ :\implies \color {red} \boxed{ \tt x = 18 }\tt \: \: \: and \: \: \: \boxed{ \tt y = 36}$

The number of days taken by A woman is 18 days.

The number of days taken by A man be 36 days.

Required Answer,

• The number of days taken by A man and woman are 36 days and 18 days respectively.