Question

(ii) 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 l woman alone to
finish the work, and also that taken by 1 man alone.​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

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

• 3 women and 6 men can finish the work in 3 days.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The time taken by 1 woman alone to finish the work.

• The time taken by 1 man alone.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the work done by man per day be x

And work done by women per day be y

According to the 1st condition:-

2 women and 5 men can together finish an embroidery work in 4 days.

Work done by 2 women and 5 men in one day = ¼

$\rm \implies5x + 2y = \dfrac{1}{4}......(i)$

According to the 2nd condition:-

3 women and 6 men can finish the work in 3 days.

Work done by 3 women and 6 men in one day =⅓

$\rm \implies6x + 3y = \dfrac{1}{3}......(ii)$

Multiplying 3 with equation (i) and 2 with equation (ii)

$\rm \implies3\bigg(5x + 2y = \dfrac{1}{4} \bigg)$

$\rm \implies15x + 6y = \dfrac{3}{4}......(iii)$

$\rm \implies2 \bigg(6x + 3y = \dfrac{1}{3} \bigg)$

$\rm \implies12x + 6y = \dfrac{2}{3} ......(iv)$

Subtracting equation (iv) from (iii)

$\rm \implies(15x + 6y) - (12x + 6y) = \dfrac{3}{4} - \dfrac{2}{3}$

$\rm \implies15x + 6y - 12x + 6y = \dfrac{9 - 8}{12}$

$\rm \implies3x = \dfrac{1}{12}$

$\rm \implies x = \dfrac{1}{12 \times 3}$

$\rm \implies x = \dfrac{1}{36}$

Substituting x = 1/36 in equation (i)

$\rm \implies 5x + 2y= \dfrac{1}{4}$

$\rm \implies \dfrac{5}{36} + 2y= \dfrac{1}{4}$

$\rm \implies 2y= \dfrac{1}{4} - \dfrac{5}{36}$

$\rm \implies 2y= \dfrac{9 - 5}{36}$

$\rm \implies 2y= \dfrac{4}{36}$

$\rm \implies 2y= \dfrac{1}{9}$

$\rm \implies y= \dfrac{1}{18}$

We have:-

Work done by 1 man in 1 day = $\dfrac{1}{36}$

Work done by 1 woman in 1 day = $\dfrac{1}{18}$

Therefore:-

Time taken by 1 man alone to finish the work = 36 days.

Time taken by 1 woman alone to finish the work = 18 days.