Question

Eighteen men can complete a piece of work in 64 days. 9 women can complete it in 108 days, whereas 7 children can finish it in 216 days. How many days will 16 men, 9 women and 21 children together take to complete the same work?

Answer 1

Answer:

$26\frac{14}{41}$  days

Step-by-step explanation:

18 men can complete a work in = 60 days

1 man can complete a work in = 60 × 18 days

Work done by 1 man in 1 day = 1/(60 × 18)

Similarly,

Work done by 1 woman in 1 day = 1/(108 × 9)

Work done by 1 child in 1 day = 1/(216 × 7)

Therefore,

Work one by 16 men + 9 women + 21 children in one day

$=\frac{16}{60\times18} +\frac{9}{108\times9} +\frac{21}{216\times7}$

$=\frac{2}{15\times9} +\frac{1}{12\times9} +\frac{1}{8\times9}$

$=\frac{1}{9} (\frac{2}{15} +\frac{1}{12} +\frac{1}{8} )$

$=\frac{1}{9} (\frac{16+10+15}{120})$

$=\frac{1}{9} \times\frac{41}{120}$

$=\frac{41}{1080}$

Thus 16 men + 9 women + 21 children will comlete the work in 1080/41 or

$26\frac{14}{41}$ days

Answer 2

Answer:27

Step-by-step explanation:

men's.

16/64x18

Female

9/108x9

Children

21/216x7

LCM =216

3+2+3/216 = 8/126 = 27 Days Answer