A and B can complete a work in 1.8 days. However, if A works alone, th

1.	A and B can complete a work in 1.8 days. However, if A works alone, then half of the work is done and he takes a break and then B alone finishes the remaining work, it takes 3.75 days to complete the work. If B is more efficient than A, how much time would B have taken to complete this task himself?1. 3.32. 2.253. 3.04. 2.7
Answer» Correct Answer - Option 3 : 3.0 Given: A and B can complete a work in 1.8 days. A completes the half work and B completes the other half work and it takes 3.75 days to complete the work. B is more efficient than A. Calculation: Let A works for ‘a’ days to complete the half of the job. Hence, B takes (3.75 – a) days to complete the remaining half of the work ∴ A’s one day work = 1/2a ∴ B’s one day work = 1/[2(3.75 – a)] Amount of work done by A and B in 1 day = 1/1.8 = 5/9 ⇒ 1/2a + 1/[2(3.75 – a)] = 5/9 ⇒ 1/a + 1/(3.75 – a) = 10/9 ⇒ (3.75 – a + a)/(a)(3.75 – a) = 10/9 ⇒ 9 × 3.75 = 10 × (a)(3.75 – a) ⇒ 33.75 = 37.5a – 10a² ⇒ 10a² – 37.5a + 33.75 = 0 ⇒ (a – 2.25)(a – 1.5) = 0 ⇒ a = 2.25, 1.5 As B is more efficient, A will take more days to complete the work a = 2.25 ⇒ B’s one day work = 1/[2(3.75 – a)] = 1/3 ∴ B will take 3 days to complete the task himself.

A and B can complete a work in 1.8 days. However, if A works alone, then half of the work is done and he takes a break and then B alone finishes the remaining work, it takes 3.75 days to complete the work. If B is more efficient than A, how much time would B have taken to complete this task himself?1. 3.32. 2.253. 3.04. 2.7

Answer» Correct Answer - Option 3 : 3.0

Given:

A and B can complete a work in 1.8 days.

A completes the half work and B completes the other half work and it takes 3.75 days to complete the work.

B is more efficient than A.

Calculation:

Let A works for ‘a’ days to complete the half of the job.

Hence, B takes (3.75 – a) days to complete the remaining half of the work

∴ A’s one day work = 1/2a

∴ B’s one day work = 1/[2(3.75 – a)]

Amount of work done by A and B in 1 day = 1/1.8 = 5/9

⇒ 1/2a + 1/[2(3.75 – a)] = 5/9

⇒ 1/a + 1/(3.75 – a) = 10/9

⇒ (3.75 – a + a)/(a)(3.75 – a) = 10/9

⇒ 9 × 3.75 = 10 × (a)(3.75 – a)

⇒ 33.75 = 37.5a – 10a²

⇒ 10a² – 37.5a + 33.75 = 0

⇒ (a – 2.25)(a – 1.5) = 0

⇒ a = 2.25, 1.5

As B is more efficient, A will take more days to complete the work

a = 2.25

⇒ B’s one day work = 1/[2(3.75 – a)] = 1/3

∴ B will take 3 days to complete the task himself.