Question

A can do a piece of work in the same time in which B and C together can do it. If
A and B together can do it in 10 days and C alone in 50 days, in how many days
can B alone do it?
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Answer 1

Answer:

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in: A. So, B alone could do the work in 25 days.

Step-by-step explanation:

Let W denotes the whole given work.

According to given data,

(i) A can complete the work W in the same time in which B & C together can complete it.

(ii) A & B together can complete the work W in 10 days.

(iii) C alone can complete the work W in 50 days. Hence,

(iv) C in 1 day can complete the amount of work = W/50

(v) Let a & b denote the times (in days) in which A & B alone can complete the work W respectively. Hence,

(vi) A & B alone in 1 day can complete the amounts of work W/a & W/b respectively.

From (i), (iv) & (vi)we get following relation,

W/a = W/b + W/50

or 1/a = 1/b + 1/50 …… (1a)

From (ii) & (vi) we get following relation,

10*(W/a + W/b) = W

or 1/a + 1/b = 1/10 …… (1b)

Hence from (1a) & (1b) we get,

1/b + 1/50 + 1/b = 1/10

or 2/b = 1/10 - 1/50

or 2/b = 4/50 or b = 50/2 = 25 (days)

Therefore it is evident from above that

B alone can complete the whole given work in 25 days