Question

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Maths Question for Genius here!
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Two women and five 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 one woman alone to finish the work, and also time taken by one man alone. ​

Answer 1

$\huge \bf{ \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}}$

let the women can finish work in

x days

and

let the men can finish work in y days

Hence.

$\sf{one \: women \: one \: day \: work = \frac{1}{x} }$

$\sf{one \: man \: one \: day \: work = \frac{1}{y} }$

$\sf{2women \: one \: day \: work = \frac{2}{x} }$

$\sf{5men \: one \: day \: work = \frac{5}{y}}$

case 1

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

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

case 2

$\sf{3women \: one \: day \: work = \frac{3}{x} }$

$\sf{6men \: 1day \: work = \frac{6}{y} }$

$\sf{3( \frac{3}{x} + \frac{6}{y} ) = 1}$

$\sf{ \frac{3}{x} + \frac{6}{y} = \frac{1}{3} ......(2)}$

let

1/x be a and 1/y be b.

→ 2a+5b=1/4......(3)

→ 3a+6b=1/3......(4)

multiply equation (3)×3 and (4)×2

→ 6a+15b=3/4.....(5)

→ 6a+12b=2/3.....(6)

→ sub eq (6) by(5)

→ 15a-12b=3/4-2/3

→ 3b=1/12

→ b=1/36

→ put value of b in eq (4)

→ 3a+6(1/36)=1/3

→ 3a=1/3-1/6=1/6

→ a=1/18

→ 1/x =1/18

$\huge{ \bf{ x=18}}$

and

1/y=1/36

$\huge{ \bf{y=36}}$

Answer 2

Answer :-

→ A women can finish the work in 18 days, and a man can finish the work in 36 days.

Step-by-step explanation :-

→ Let a women can finish the work in x days.

→ While, a man alone can do it in y days.

▶ Now,

A/Q,

$\implies { \frac{2}{x} + \frac{5}{y} = \frac{1}{4} . }$

Let $\sf{ \frac{1}{x} = u \: and \: \frac{1}{y} = v }$

$\implies 2u + 5v =\sf{ \frac{1}{4} . }$ . ...........(1).

And,

$\implies \sf{ \frac{3}{x} + \frac{6}{y} = \frac{1}{3} . }$

$3u + 6v =\sf{ \frac{1}{3} . }$ . ...........(2).

➡ Multiply equation (1) by 3 and equation (2) by 2, we get

$\implies 6u + 15v =\sf{ \frac{3}{4} . }$ . ...........(3).

$\implies 6u + 12v =\sf{ \frac{2}{3} . }$ . ...........(4).

➡ On substracting equation (3) and (4), we get

$\implies 3v = \sf{ \frac{3}{4} - \frac{2}{3} = \frac{9-8}{12} = \frac{1}{12}. }$ .

So, $\implies v = \sf{ \frac{1}{36} }$

and from equation (1).

$\implies 2u = \sf{ \frac{1}{4} - \frac{5}{36} = \frac{4}{36} = \frac{1}{9} }$

$\implies u =\sf{ \frac{1}{18} }$

Hence, x = 18 days and y = 36 days.

•°• A women can finish the work in 18 days, and a man can finish the work in 36 days.