A is twice as efficient as B and therefore completes a piece of work i

1.	A is twice as efficient as B and therefore completes a piece of work in 20 days less than what B takes to complete the same work. the time in which they can complete the work working together is?1. 13 days2. \(13\frac12\) days3. 14 days4. \(13\frac13\)days5. 15 days
Answer» Correct Answer - Option 4 : \(13\frac13\)days Given: The efficiency of A = 2 × efficiency of B Time taken by A = time taken by B - 20 Concept used: Time = (Total work)/(Efficiency) 1.) When work is the same the ratio of time and efficiency is inversely proportional. eg - if time = 3 : 4 then, efficiency = 4 : 3 2.) The time required to complete the work is the reciprocal of the fraction of work done in one time period (one day). Calculation: Efficiency → A : B = 2 : 1 Time taken → A : B = 1 : 2 Difference in time = 2 - 1 = 1 ratio ∴ 1 ratio = 20 days A's time = 20 days B's time = 40 days (A + B)'s one day work = \(\frac{1}{20}+\frac{1}{40}=\frac{3}{40}\) Time taken to complete the work = \(\frac{40}{3}=13\frac13days\) ∴ Time taken to complete the work is \(13\frac13days\)

A is twice as efficient as B and therefore completes a piece of work in 20 days less than what B takes to complete the same work. the time in which they can complete the work working together is?1. 13 days2. \(13\frac12\) days3. 14 days4. \(13\frac13\)days5. 15 days

Answer» Correct Answer - Option 4 : \(13\frac13\)days

Given:

The efficiency of A = 2 × efficiency of B

Time taken by A = time taken by B - 20

Concept used:

Time = (Total work)/(Efficiency)

1.) When work is the same the ratio of time and efficiency is inversely proportional. eg - if time = 3 : 4 then, efficiency = 4 : 3

2.) The time required to complete the work is the reciprocal of the fraction of work done in one time period (one day).

Calculation:

Efficiency → A : B = 2 : 1

Time taken → A : B = 1 : 2

Difference in time = 2 - 1 = 1 ratio

∴ 1 ratio = 20 days

A's time = 20 days

B's time = 40 days

(A + B)'s one day work = \(\frac{1}{20}+\frac{1}{40}=\frac{3}{40}\)

Time taken to complete the work = \(\frac{40}{3}=13\frac13days\)

∴ Time taken to complete the work is \(13\frac13days\)