A and B together can do a piece of work in 18 days and B and C can do

1.	A and B together can do a piece of work in 18 days and B and C can do the same work together in 24 days. If the efficiency ratio of A and C is 2 : 1 then in how much time can B alone do the work? 1. 182. 483. 244. 36
Answer» Correct Answer - Option 4 : 36 Given: A and B together can do a piece of work in 18 days and B and C can do the same work together in 24 days. The efficiency ratio of A and C is 2 : 1 Concept Used: Total work = LCM of separate time taken to finish the work Calculation: A and B together can do a piece of work in 18 days and B and C can do the same work together in 24 days. LCM of 18 and 24 is 72 ⇒ Total work is 72 units In 1 hour A and B together can do 72/18 = 4 unit work ----(1) In 1 hour B and C together can do 72/24 = 3 unit work ----(2) The ratio of efficiency of A and C is 2 : 1 Let, in 1 hour A can do 2 unit work and C can do 1 unit work ----(3) Using (1) and (3) get, B can do 2 unit work in 1 hour, which satisfies (2) [∵ A = 2 & B = 2 ⇒ A + B = 4 and B = 2 & C = 1 ⇒ B + C = 3] B alone can do 2 unit work in 1 hour ⇒ To do 72 unit work B alone will take 72/2 = 36 hours ∴ In 36 hour B alone can do the work.

A and B together can do a piece of work in 18 days and B and C can do the same work together in 24 days. If the efficiency ratio of A and C is 2 : 1 then in how much time can B alone do the work? 1. 182. 483. 244. 36

Answer» Correct Answer - Option 4 : 36

Given:

A and B together can do a piece of work in 18 days and B and C can do the same work together in 24 days. The efficiency ratio of A and C is 2 : 1

Concept Used:

Total work = LCM of separate time taken to finish the work

Calculation:

A and B together can do a piece of work in 18 days and B and C can do the same work together in 24 days.

LCM of 18 and 24 is 72

⇒ Total work is 72 units

In 1 hour A and B together can do 72/18 = 4 unit work ----(1)

In 1 hour B and C together can do 72/24 = 3 unit work ----(2)

The ratio of efficiency of A and C is 2 : 1

Let, in 1 hour A can do 2 unit work and C can do 1 unit work ----(3)

Using (1) and (3) get, B can do 2 unit work in 1 hour, which satisfies (2)

[∵ A = 2 & B = 2 ⇒ A + B = 4

and B = 2 & C = 1 ⇒ B + C = 3]

B alone can do 2 unit work in 1 hour

⇒ To do 72 unit work B alone will take 72/2 = 36 hours

∴ In 36 hour B alone can do the work.