Question

A & B working together completes a job in 24 days. If A complete half of the work alone and B completes the remaining work, the work will be completed in 64 days. What is the difference between the time taken by A and B to complete the work alone?​

Answer 1

Answer:

Solution of the given problem is shown below,

Let W denotes the whole given work.

According to given data,

(i) A & B working together can complete the work W in 24 days.

(ii) If A completes the work W/2 alone and B completes the remaining work W/2, the work will be completed in 64 days.

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

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

(v) Let D denotes the difference between the time taken by A and B to complete the work W alone.

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

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

or 1/a + 1/b = 1/24 …… (1a)

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

(W/2)/(W/a) + (W/2)/(W/b) = 64

or a/2 + b/2 = 64 or a + b = 128 or b = 128 - a …… (1b)

From (1a) & (1b) we get,

1/a + 1/(128 - a) = 1/24

or a^2 - 128*a + 64^2 = 64*(64 - 48)

or (a - 64)^2 = 64*16 or a - 64 = 8*4 = 32 or a = 96 (days) …… (1c)

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

b = 128 - a = 128 - 96 = 32 (days) …… (1d)

Therefore from (v), (1c) & (1d) we get,

D = a - b = 96 - 32 = 64 (days) [Ans]

Step-by-step explanation:

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