Question

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

Answer 1

Answer:

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}

4

1

----------(1)

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

4m + 4w = \frac{1}{3}

3

1

-----------(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}

3

1

−

2

1

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

6

1

6w = \frac{1}{6}

6

1

w = \frac{1}{36}

36

1

One lady can complete one work in 36 days

Now put the value of w in equation (2)

4m + 4(\frac{1}{36}

36

1

) = \frac{1}{3}

3

1

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

9

1

=

3

1

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

3

1

−

9

1

4m = \frac{2}{9}

9

2

m = \frac{1}{18}

18

1

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.