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 together for 10 days when B and C leave. How many days more will A take to finish the work ?
Answers
Answer:
(A + B)’s one days’ work = 1/30
(B + C)’s one days’ work = 1/24 .....(1)
(C + A)’s one days’ work = 1/20
Therefore (A + B + C)’s one days’ work
(A + B + C)’s 10 days’ work
= 10/6 = 5/8
From (1) and (2), A's one days’ work
= 1/16 – 24
= 1/48
Therefore remaining 3/8 of the work is done by A alone in 3/8 × 48
= 18 days.
Answer:
(A+B)'s one day's work =
30
1
(B+C)'s one day's work =
24
1
..........(1)
(C+A)'s one day's work =
20
1
∴(A+B+C)'s one day's work =
2
1
[
30
1
+
24
1
+
20
1
]=
2
1
×[
600
20+25+30
]=
1200
75
=
16
1
...........(2)
(A+B+C)'s 10 day's work =
16
10
=
8
5
Remaining work, 1−
8
5
=
8
3
(which is done by A)
From (1) and (2), A's one day's work =
16
1
−
24
1
=
48
1
∴ Remaining
8
3
of the work is done by A alone in
8
3
×48=18 days.
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