Question

10men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days .If all the 10 men and 15 women work together ,in how many days will the work get completed​

Answer 1

Work done by 10 man in 1 day = 1 / 15

Work done by 15 woman in 1 day = 1 / 12

Therefore,

Work done by 10 man and 15 woman in 1 day =

$\frac{1}{15} + \frac{1}{12} = \frac{27}{180} = \frac{3}{2}$

Therefore, If 10 men and 15 woman work together then the work will be finished in 2/3 days

Answer 2

Given data :-

• 10 mens can complete a piece of work in 15 days.
• 15 womens can complete the same work in 12 days.
• All the 10 men and 15 women work together and completed their work.

Solution :-

Let, total work be 100 and days taken by 10 men and 15 women completed their work together in be x

→ Let, 10 men complete their work in one day = 1/15 work.

→ Let, 15 men complete their work in one day = 1/12 work.

→ 10 men and 15 women work together

and completed their work in one day

= 1/15 + 1/12

→ 10 men and 15 women work together

and completed their work in one day

= {1×12}/{15×12} + {1×15}/{12×15}

→ 10 men and 15 women work together

and completed their work in one day

= 12/180 + 15/180

→ 10 men and 15 women work together

and completed their work in one day

= {12+15}/180

→ 10 men and 15 women work together

and completed their work in one day

= 27/180

→ 10 men and 15 women work together

and completed their work in one day

= 3/20 work

→ 10 men and 15 women complete their work from total days = {3/20} × 100

→ 10 men and 15 women complete their work from total days = 0.15 × 100

→ 10 men and 15 women work together

and completed their work in one day in percent = 15 work

Now, according to assumption

→ x = 100/15

→ x = 20/3 day or

→ x = 6 ⅔ day

Hence, all the 10 men and 15 women work together and complete their work in 6 ⅔ days.