Question

A is three times more efficient worker than B and is therefire able to complete a work in 60 days less than B. What is the number of days that A and B together will take to complete the work ?​

Answer 1

Let B take b days to complete a job. So A takes (b-60) days to complete the same job.

B does (1/b)th part of the work in a day, while A does (3/b)th part of the work in a day.

So we have A doing [1/(b-60)]th or (3/b)th part of the work in a day.

So equation the two we get [1/(b-60)] = (3/b), or

b = 3b - 180, or

180 = 2b, or b = 90 days. So A takes 90–60 = 30 days.

A does (1/30)th part of the work in a day while B does (1/90)th part of the work in a day. A and B together will do (1/30)+(1/90) = (3/90)+(1/90) = 4/90)th part of the work in a day.

So A and B will complete the work in 22.5 days, working together.

Answer 2

Answer:

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Let B complete the work in x days. Then,

A will complete the same work in x/3 days.

Given, x – x/3 = 60

=> 2x/3 = 60

=> x = 60 × 3/2 = 90 days.

Therefore A will complete the work in 30 days.

(A + B)'s 1 days' work

= 1/90 + 1/30

= 4/90

=> (A + B) will complete the whole work in 90/4

= 22.5 days.