P is 40% less efficient than Q and Q, R together can complete a piece of work in 12 days. If P and Q together started the work and after 6 days

R also joined them, then in next 4 days the whole work gets completed. In how many days P alone can complete the whole work?

Let’s break down the problem step by step.

### Step 1: Define efficiencies
Let’s assume the efficiency of Q is \( E_Q \) (the amount of work Q can do in one day).  
Since P is 40% less efficient than Q, the efficiency of P is:
\[
E_P = 0.6 \times E_Q
\]
Let the efficiency of R be \( E_R \).

### Step 2: Work done by Q and R together
It is given that Q and R together can complete the whole work in 12 days. Therefore, the combined efficiency of Q and R is:
\[
E_Q + E_R = \frac{1}{12} \quad \text{(since the total work is 1 and they complete it in 12 days)}
\]

### Step 3: Work done by P, Q, and R
- P and Q work together for the first 6 days. So, in these 6 days, the total work done by them is:
\[
\text{Work by P and Q in 6 days} = 6 \times (E_P + E_Q) = 6 \times (0.6E_Q + E_Q) = 6 \times 1.6E_Q = 9.6E_Q
\]
- After 6 days, R joins P and Q. Now, P, Q, and R work together for 4 more days. In these 4 days, the work done is:
\[
\text{Work by P, Q, and R in 4 days} = 4 \times (E_P + E_Q + E_R) = 4 \times (0.6E_Q + E_Q + E_R) = 4 \times (1.6E_Q + E_R)
\]
Substitute \( E_Q + E_R = \frac{1}{12} \):
\[
\text{Work by P, Q, and R in 4 days} = 4 \times (1.6E_Q + \frac{1}{12} - E_Q) = 4 \

P is 40% less efficient than Q and Q, R together can complete a piece of work in 12 days. If P and Q together started the work and after 6 days R also joined them, then in next 4 days the whole work gets completed. In how many days P alone can complete the whole work?

Solve a complex work and time efficiency problem where P is 40% less efficient than Q. Q and R can finish work in 12 days, but when P, Q, and R work together, the whole job gets done in 4 more days. Detailed step-by-step breakdown of the solution included.

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