Question

A and B together can complete a task in 1.2 days. However, A starts working
alone and left the work on completion of half of the work, then B alone completes
the remaining half of the work. Thus it takes 2.5 days to complete the work. If Bis
more skilled than A and B alone finishes the work from start to finish, then how
many days will it take?
(a) 1.5 (b)2.2
(c)2.0 (d) 1.8​

Answer 1

The correct answer is c) 2.0

Suppose, A can complete the task in = x days,

B can complete the task in = y days

According to the question,

1/x + 1/y = 1/1.2

⇒ x + y = xy/1.2 ...i)

A completes half the job in = x/2 days and B completes half the job in = y/2 days

⇒ x/2 + y/2 = 2.5

⇒ x + y = 5 ...ii)

From (i) and (ii), we get,

xy/1.2 = 5

⇒ xy = 6

⇒ x = 6/y ...iii)

From (ii) and (iii) we get,

6/y + y = 5

⇒ 6 + y2 = 5y

⇒ y2 – 3y – 2y + 6 = 0

⇒ y(y – 3) – 2(y – 3) = 0

⇒ (y – 3) (y – 2) = 0

⇒ y = 3 or 2

For y = 3, x = 6/3 = 2

For y = 2, x = 6/2 = 3

∵ B is more efficient than A

∴ B take less days than A

∴ B would take 2 days to complete the task

Hope it helps....