Question

two 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 one woman alone to finish the work, and also time taken by one man alone.

Answer 1

$<b> <u>$
Hey there !!


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

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


▶ Now,

A/Q,

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


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


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


▶ And,


=> $\bf{ \frac{3}{x} + \frac{6}{y} = \frac{1}{3} . }$


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



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


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

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


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

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

So, => v = $\bf{ \frac{1}{36} }$


and from equation (1).

=> 2u = $\bf{ \frac{1}{4} - \frac{5}{36} = \frac{4}{36} = \frac{1}{9} }$

=> u =$\bf{ \frac{1}{18} }$


✔✔ 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.

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THANKS



#BeBrainly.

Answer 2

$\huge \bf{hey}$

$\huge{here \: is \: answer}$


$<b> <I> let the number of women be x and no of men be y [tex] \sf{one \: women \: one \: day \: work = \frac{1}{x} }$


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


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

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

x=18

and


1/y=1/36

y=36

$\huge{hope \: it \: helps}$

$\huge{ \mathfrak{thanks}}$