1. A and B can complete the work in 10 and 20 days respectively. They started doing the work together but after 5 days B had to leave and A alone completed the remaining work. The whole work was completed in:
Solution:
Their 1 day’s work = 1/10 +1`/20 = 3/20.
Their 5 day’s work = 5(3/20) = 3/4.
Remaining work which is to be done by A = 1 – 3/4 = 1/4.
It is done by A in (10*1/4) = 5/2.
The whole work is completed in (5+5/2) = 7.5 days.
2. A and B can do a piece of work in 10 days, while B and C can do the same work in 20 days C and A in 30 days. They all work together for 6 days when B and C leave. How many days more will A take to finish the work?
Solution:
2(A+ B+ C) = 1/10 + 1/20 + 1/30 = 11/60
1 day’s work of (A+ B+ C) = 11/120
They all work for 6 days = 6(11/120) = 11/20.
Remaining work which is to be done by A = 1 – 11/20 = 9/20.
A’s 1 day’s work = (A+ B+ C) – (B+ C) = 11/120 -1/20 = 1/24.
Remaining work which is to be done by A in 24*(9/20) = 10(4/5) days.
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