а 6. A and B can do a piece of work in 40 days, B and C in 30 days and C and A in 24 days. (a) How long will it take them to do the work together? (b) In what time can each finish it working alone?
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Answer:
Correct option is C)
A and B can do a piece of work in 40 days
(A + B)'s 1 day's work =
40
1
-- (1)
B and C in 30 days
(B + C)'s 1 day's work =
30
1
---- (2)
C and A in 24 days.
(C + A)'s 1 day's work =
24
1
--- (3)
Adding 1,2,3
2(A+B+C) =
40
1
+
30
1
+
24
1
=
1200
120
=
10
1
So, (A + B + C)'s 1 day's work =
20
1
-- - (4)
(4)−(2) A =
20
1
−
30
1
=
60
1
(4)−(3) B =
20
1
−
24
1
=
120
1
(4)−(1) C =
20
1
−
40
1
=
40
1
Hence, A will take 60 days, B will take 120 days and C will take 40 days to do the work alone.
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