Correct Answer - Option 1 : 156/5 days
Given:
A house can be painted by A in 39 days, by B in 52 days, and by all in 13 days.
Concept Used:
As A can do a piece of work in 50 days and (A + B) can do the same work in 20 days.
Concept Used:
By LCM method we are going to prove how it works
Step 1:
Find the least common multiple for all the given days/hours/minutes.
Step 2:
The least common multiple found in step 1 is considered as the total amount of work to be completed.
Step 3:
Use the formula given below to solve the problem.
Number of days = (Total work is done in units/Number of units completed per day)
Number of units completed per day = (Total work is done in units/Number of days)
Calculation:
By using the above-mentioned formula
LCM of 39, 52, 13 days is 156 unit (Total work)
The efficiency of A will be
⇒ A(E) = 156/39 = 4 unit/day
Similarly, the efficiency of B will be
⇒ B(E) = 156/52 = 3 unit/day
The efficiency of (A + B + C) will be
⇒ (A + B + C)(E) = 156/13 = 12 unit/day
The efficiency of C = (A + B + C) – A – B = 12 – 4 – 3 = 5 unit/day
The time taken by C to complete the work alone will be
⇒ 156/5 days
∴ The time by C alone to finish the work is 156/5 days
