Question

A , B and c can do a piece of work in 10 days ,12 days and 15 days respectively how long will they take to finish it if they work together

Answer 1

ABand C can do a piece of work in 1/10,1/12,1/15
1/10+1/12+1/15
C can do work in 4 days

Answer 2

Let the work be completed in x days.

A's 1 days' work = ⅒

⇒A's (x−5) days' work =(x-5)/10

B's 1 days' work = 1/12

⇒B's (x−3) days' work = (x−3)/12

C's 1 days' work = 1/15

⇒C's x days' work = x/15

$⇒ \frac{x - 5}{10} + \frac{x - 3}{12} + \frac{x}{15}$

$⇒ \frac{6(x−5)+5(x−3)+4x}{60}=1$

$⇒6x−30+5x−15+4x=60$

$⇒15x=60+45=105⇒x = 7$

∴ The work was completed in 7 days.