A can paint a house in 39 days and B can paint the same house in 52 days, with the help of C they can paint the house in 13 days. How much C time will C take to paint the house alone?

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**