55. A and B can do a piece of work in 30 days while B and C
can do the same work in 24 days and C and A in 20 days.
They all work for 10 days and B and C leave. How many
days more will A take to finish the work?
(a) 12
(b) 18
(c) 20
(d) 22
the
dist
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(a)
(C)
Directid
Answers
Let the number of days taken by A, B & C to complete the work individually be a, b & c respectively.
Given, A and B can do a piece of work in 30 days
=> 1/a + 1/b = 1/30
Given, B and C can do the same work 24 days
=> 1/b + 1/c = 1/24
Given, A and C can do the same work in 20 days
=> 1/c + 1/a = 1/20
Adding all the three equations,
=> 2(1/a +1/b + 1/c) = 1/30 + 1/24 + 1/20 = (20+25+30)/600 = 75/600 = 1/8
=> 1/a + 1/b + 1/c = 1/16
=> When A, B & C work together, the amount of work done in one day is 1/16
(1/a + 1/b + 1/c) - (1/b + 1/c) = 1/16 - 1/24 = (3–2)/48 = 1/48
=> 1/a = 1/48
=> The work done by A individually in one day = 1/48
Given that A, B & C work together for 10 days,
=> Work done by them together for 10 days = 10 * (1/16) = 10/16 = 5/8
=> The remaining work to be done by A alone = 1–5/8 = 3/8
The number of days taken by A alone to complete the remaining work = (3/8)/(1/48) = 18 days