Question

If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?

Answer 1

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▶ Question - If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?




▶ Explanation :-



Let 1 man can finish the work in x days


And 1 woman can finish the work in y days


=> 1 man's one day work = 1 / x


∴ 2 men's one day work = 2 / x


=> 1 woman one day work = 1 / y


∴ 3 women one day work = 3 / y


( 2 men + 3 women )'s one day work = 2 / x + 3 / y


= 2y + 3x / xy


Number of days required for 2 men and 8 women to finish the work = xy / 2y + 3x


=> xy / 2y + 3x = 8


=> xy = 8 ( 2y + 3x )


=> xy = 16y + 24x --------- ( 1 )


Number of days required for 3 men and 2 women to finish the work = xy / 2x + 3y


=> xy / 2x + 3y = 7


=> xy = 7 ( 2x + 3y )


=> xy = 14x + 21y -------- ( 2 )



On comparing equations ( 1 ) and ( 2 ), we get :-


=> 16y + 24x = 14x + 21y


=> 16y - 21y = 14x - 24x


=> - 5y = - 10x


=> 5y = 10x


=> y = 2x



Substituting value of y in equation ( 2 ) we get



=> x × 2x = 14x + 21 × 2x


=> 2x^2 = 14x + 42x


=> 2x^2 = 56x


=> 2x = 56


=> x = 56 / 2


=> x = 28


Substituting value of x in y we get :-


=> y = 2 × 28


=> y = 56


∴ 1 man can finish the work in 28 days and 1 woman can finish the work in 56 days



∴ ( 5 men + 4 women )'s one day work = 5 / x + 4 / y


= 5y + 4x / xy


= 5 × 56 + 4 × 28 / 28 × 56


= 280 + 112 / 1568


= 392 / 1568


= 1 / 4



∴ 5 men and 4 women can do the work in 4 days.




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Answer 2

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______Here's your Answer ____________

Let 1 man can finish the work in x days

And 1 woman can finish the work in y days

=> 1 man's one day work = 1 / x

∴ 2 men's one day work = 2 / x

Similarly,

=> 1 woman one day work = 1 / y

∴ 3 women one day work = 3 / y

( 2 men + 3 women )'s one day work = 2 / x + 3 / y

= 2y + 3x / xy

Number of days required for 2 men and 8 women to finish the work = xy / 2y + 3x

=> xy / 2y + 3x = 8

=> xy = 8 ( 2y + 3x )

=> xy = 16y + 24x --------- (1)


Number of days required for 3 men and 2 women to finish the work = xy / 2x + 3y

=> xy / 2x + 3y = 7

=> xy = 7 ( 2x + 3y )


=> xy = 14x + 21y --------(2)

On comparing equations (1) and (2), we get :-

=> 16y + 24x = 14x + 21y

=> 16y - 21y = 14x - 24x

=> - 5y = - 10x

=> 5y = 10x

=> y = 2x ------------------(3)

Substituting value of y in equation ( 2 ) we get

=> x × 2x = 14x + 21 × 2x

=> 2x^2 = 14x + 42x 

=> 2x^2 = 56x 

=> 2x = 56

=> x = 56 / 2

=> x = 28

Putting x = 28 in equation 3.we get,

=> y = 2 × 28

=> y = 56

So , 1 man can finish the work in 28 days and 1 woman can finish the work in 56 days

∴ ( 5 men + 4 women )'s one day work = 5 / x + 4 / y

= 5y + 4x / xy

= 5 × 56 + 4 × 28 / 28 × 56

= 280 + 112 / 1568

= 392 / 1568

= 1 / 4.
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