A sells an article to B making a profit of `(1)/(5)` fot his outlay. B sells it to C, going 20%. If C sells it for Rs 600 and incurs a loss of `(1)/(6)` of his outlays, the cost price of A is

Answer

To solve the problem step by step, let's denote the cost price of A as \( CP_A \), the cost price of B as \( CP_B \), and the cost price of C as \( CP_C \).

### Step 1: Understand the Profit and Loss Percentages
- A sells to B with a profit of \( \frac{1}{5} \) of his outlay. This means if A's cost price is \( CP_A \), then:
\[ CP_B = CP_A + \frac{1}{5} CP_A = \frac{6}{5} CP_A \]

- B sells to C at a profit of 20%. Therefore:
\[ CP_C = CP_B + 0.2 \times CP_B = 1.2 \times CP_B = 1.2 \times \frac{6}{5} CP_A = \frac{7.2}{5} CP_A \]

### Step 2: Determine C's Selling Price and Loss
- C sells the article for Rs 600 and incurs a loss of \( \frac{1}{6} \) of his outlay. This means:
\[ Selling Price = CP_C - \frac{1}{6} CP_C = \frac{5}{6} CP_C \]

Setting the selling price equal to Rs 600:
\[ \frac{5}{6} CP_C = 600 \]

### Step 3: Solve for \( CP_C \)
To find \( CP_C \):
\[ CP_C = 600 \times \frac{6}{5} = 720 \]

### Step 4: Substitute \( CP_C \) Back to Find \( CP_A \)
Now, we know:
\[ CP_C = \frac{7.2}{5} CP_A \]
Substituting \( CP_C = 720 \):
\[ 720 = \frac{7.2}{5} CP_A \]

To find \( CP_A \):
\[ CP_A = 720 \times \frac{5}{7.2} = 720 \times \frac{5}{7.2} = 720 \times \frac{5}{7.2} = 720 \times \frac{25}{36} = 500 \]

### Conclusion
The cost price of A is Rs 500.