Question

A alone would take 32 hours more to complete a work than A and B together. B takes 18 hours more to complete a work alone than A and B together. In 9 hours how much percent work A and B can complete working together?​

Answer 1

Answer:

Step-by-step explanation:

Solution of the given problem is shown below,

Let W denotes the whole given work.

According to given data,

(i) A alone would take 27 hours more to complete the work W than if both A & B worked together.

(ii) If B worked alone, he took 3 hours more to complete the work W than A & B worked together.

(iii) Let D denotes the time (in hours) that A & B would take to complete the work W if both A & B worked together.

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

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

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

a = 27 + D …… (1a)

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

b = 3 + D …… (1b)

From (iii) & (v) we get following relation,

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

or 1/D = 1/a + 1/b

or 1/D = 1/(27 + D) + 1/(3 + D) [from (1a) & (1b)]

or 1/D - 1/(27 + D) = 1/(3 + D)

or 27*(3 + D) = D*(27 + D)

or D^2 = 81 or D = 9 (hrs)

Therefore from above it is evident that

A & B together will complete the whole given work in 9 hours