Question

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If A and B can do a piece of work in 24 days, B and C can do itin 40
In how many days can A alone do it?
o 75 days
460
23 091786077
O 120 days
O 40 days​

Answer 1

Solution of the given problem is shown below,

Let W denotes the whole given work.

Let a, b & c denote the amounts of time (in days) required by A, B & C respectively to complete the work W by working alone. Hence,

A, B & C in 1 day can complete the amounts of work respectively W/a, W/b & W/c by working alone.

It is mentioned that,

(i) A and B together can complete the work W in 40 days.

(ii) B and C together can complete the work W in 120 days.

(iii) B alone can complete the work W in 180 days.

From (i) we get the relation,

40*(W/a + W/b) = W or 1/a + 1/b = 1/40 …….. (1a)

From (ii) we get the relation,

120*(W/b + W/c) = W or 1/b + 1/c = 1/120 …….. (1b)

From (iii) we get, b = 180 (days) …….. (1c)

From (1a) & (1c) we get,

1/a = 1/40 - 1/180 = 7/360 …….. (1d)

From (1b) & (1c) we get,

1/c = 1/120 - 1/180 = 1/360 …….. (1e)

Let D denotes the time (in days) when A and C together can complete the work W. So we get the relation,

D*(W/a + W/c) = W or 1/a + 1/c = 1/D

or 1/D = 7/360 + 1/360 [from (1d) & (1e)]

or 1/D = 8/360 = 1/45 or D = 45 (days) [Ans]