Question

2 Gents and 5 Ladies complete a work in 4 days. 4 Gents and 4 Ladies takes 3
days to complete the same work. Then how many days need to complete the
same work for a single Gents or Ladies?​

Answer 1

A single gents can complete the work in 18 days and a lady in 36 days.

Step-by-step explanation:

Let one day work of a gents is represented by m

and one day work for a lady by w.

2 Gents and 5 ladies complete a work in 4 days.

2m + 5w = $\frac{1}{4}$ ----------(1)

4 Gents and 4 ladies complete a work in 3 days.

4m + 4w = $\frac{1}{3}$ -----------(2)

To calculate the value of w multiply equation (1) by 2 and subtract it from equation (2)

(4m + 4w) - (4m + 10w) = $\frac{1}{3}-\frac{1}{2}$

-6w = -$\frac{1}{6}$

6w = $\frac{1}{6}$

w = $\frac{1}{36}$

One lady can complete one work in 36 days

Now put the value of w in equation (2)

4m + 4($\frac{1}{36}$) = $\frac{1}{3}$

$4m+\frac{1}{9}=\frac{1}{3}$

4m = $\frac{1}{3}-\frac{1}{9}$

4m = $\frac{2}{9}$

m = $\frac{1}{18}$

One gents can complete the work in 18 days alone.

Therefore, single gents can complete the work in 18 days and a lady in 36 days.

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