A alone can finish the work in 10 hours, B alone can finish the work in 12 hours and C alone can finish the work in 15 hours. A, B and C together started working at 11’o clock. After 2 hours A leaves. When will B & C will together will finish the work?
Answers
Work done by A in 1-hour = (1/10)
Work done by B in 1-hour = (1/12).
Work done by C in 1-hour = (1/15).
work done by (A + B + C) in 1-hour = (1/10 + 1/12 + 1/15) = 15/60 = 1/4.
Work done by ABC in 2 hours = (1/4) * 2 = (1/2).
Amount of work left by B and C = 1 - (1/2) = 1/2.
Then,
Amount of work done by B + C :
= > (1/12 + 1/15)
= > (9/60)
= > (3/20).
Hence, the time taken by B and C on working together in 1 - hour:
= > (3/20) * (2)
= > (3/10).
Therefore, B and C will together finish the work in (10/3) hours (or) 3 (1/3) hours.
Hope it helps!
A can do the work in 10 hours
⇒ 1 hour = 1/10 of work
B can do the work in 12 hours
⇒ 1 hour = 1/12 of the work
C can do the work in 15 hours
⇒ 1 hour = 1/15 of the work
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Find the amount of work A, B and C can do in an hour:
1 hour = 1/10 + 1/12 + 1/15 = 1/4
Find the amount of work A, B and C can do in 2 hours:
1 hour = 1/4 of the work
1 hours = 1/4 x 2 = 1/2 of the work
Amount of work left to do after 2 hours :
1 - 1/2 = 1/2 of the work
Amount of work B and C can do in an hour:
one hour = 1/12 + 1/15 = 3/20 of the work
Find the number of hours B and C need to complete the work:
Number of hours needed = 1/2 ÷ 3/20 = 1/2 x 20/3 = 10/3 hours = 3h 20 mins
Find the total duration of work:
A, B and C worked for 2 hours
B and C worked for 3 hours 20 mins
Total duration = 2 hours + 3 hours 20 mins = 5 hours 20 mins
Find the time that B and C will complete the work:
Start time = 11 am
Duration = 5 hours 20 mins
End time = 4:20 pm
Answer: B and C will finish the work at 4:20pm