A can complete a work in 10 days, B in 12 days and C in 15 days. All of them began the work together but A had to leave the work after 2 days of the start and B ,3 days before the completion of the work. how long did the work last?
Answers
A completes the work in 10 days
B completes the work in 12 days
C completes the work in 15 days
A's one day's work = 1/10
B's one day's work = 1/12
C's one day's work= 1/15
A,B and C's one day's work = 1/10+1/12+1/15----------->15/60------->1/4
2(1/10) + x-3/12 + x/15 =1
12+5x-15+4x/60=1------------------------> -3+9x=60---------------------->x=63/9
x=7
The work will last for 7 days.
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answered May 15, 2019 by navnit40 (-4,939 points)
A’s one day’s work = 1/10
B’s one day’s work = 1/12
C’s one day’s work = 1/15
A, B and C’s one day’s work = 1/10 + 1/12 + 1/15
= (6 + 5 + 4)/60 = 15/60 = ¼
Let the work completed in x days
∴ A’s 2 days work + B’s (x – 3) days work + C’s x days work = 1
⇒ 2 × (1/10) + (x – 3) × 1/12 + x × (1/15) = 1
⇒ 1/5 + (x -3)/12 + x/15 = 1
(12 + 5x – 15 + 4x = 60)/60
(L.C.M of 5, 12, 15 = 60)
⇒ 9x = 60 – 12 + 15 ⇒ 9x = 63
⇒ x = 63/9 = 7
∴ Work will last for 7 days