Question

A and B can complete a work in 8 days and 15 days respectively. In how many days will both work together, if A increases his capacity by 33.33% and B increases his capacity by 25%?​

Answer 1

Answer:

Solution of the given problem is shown below,

Let W denotes the whole given work.

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

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

As per given data we have,

A takes 20 days more than B to complete the work W. So we get the following relation,

a = b + 20 …… (1)

If A increases his capacity by 25% and B decreases his capacity by 33.33% then A takes 5 days more than B to complete the work W.

Let ac & bc denote the numbers of days required for A & B respectively to complete the work W separately at their changed capacities.

So we get the following relations,

1/ac = (1 + 25/100)*(1/a) = 1.25/a …… (2a)

1/bc = (1 - 33.33/100)*(1/b) = 0.6667/b …… (2b)

ac = bc + 5 …… (2c)

From (2a), (2b) & (2c) we get,

a/1.25 = b/0.667 + 5

or (b + 20)/1.25 = b/0.667 + 5 [from (1)]

or b/0.667 - b/1.25 = 20/1.25 - 5

or b*(1.5 - 0.8) = 16 - 5 = 11 or b = 11/0.7 = 110/7 (days) …. (3)

Therefore from (1) & (3) we get,

a = b + 20 = 110/7 + 20 = 250/7 = 35 (5/7) (days) [Ans]