2ladies and 5 gents can complete an embroidery work in 4 days 3 ladies and 6 gents can complete it in 3 days find how many days a single lady can take to complete it again how much time a single man can complete it

Step-by-step explanation:

Let the time taken by one man alone and one women alone to do the work be a and b respectively.

Amount of work done by one man in a day = 1/a

Amount o work done by 5 men in a day = 5/a

Amount of work done by one lady in a day = 1/b

Amount of work done by 2 ladies in a day = 2/b

CASE 1

According to the question

2/b + 5/a = 1/4. -(1)

Simialrily in case 2

3/b + 6/a = 1/3. -(2).

In eq 1 and 2

Let 1/b be x and 1/a be y.

Therefore the new equations are

2x + 5y = 1/4

= 8x + 20y = 1. -(3)

Also

3x + 6y = 1/3

= 9x + 18y = 1. -(4)

On using elimination method for equations 3 and 4

x = 1/18 = 1/b

= b =18

And y = 1/36 = 1/a

= a = 36

Therefore the time taken by one man and one woman alone to do the work is 36 days and 18 days respectively.

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