A watch passes through three hands and each gains 25%. If the third sells it for Rs. 250, what did the first pay for it?

Options

A. 128
B. 130
C. 145
D. 150

Answer

To solve the problem step by step, we will determine the cost price (CP) of the watch for the first person (A) based on the selling price (SP) of the third person (C) and the gain percentage.

### Step 1: Understand the Gain Percentage
Each person gains 25% on the cost price. We can express this gain as a fraction:
- Gain of 25% = 25/100 = 1/4
- Therefore, if the cost price is \( CP \), the selling price \( SP \) can be calculated as:
\[ SP = CP + \text{Gain} = CP + \frac{1}{4}CP = \frac{5}{4}CP \]

### Step 2: Set Up the Selling Price for Each Person
Let’s denote:
- \( CP_A \) = Cost price for the first person (A)
- \( CP_B \) = Cost price for the second person (B)
- \( CP_C \) = Cost price for the third person (C)

From the gain formula, we can express the selling prices:
- Selling price for A (to B):
\[ SP_A = \frac{5}{4}CP_A \]
- Selling price for B (to C):
\[ SP_B = \frac{5}{4}CP_B \]
- Selling price for C (final selling price):
\[ SP_C = \frac{5}{4}CP_C \]

### Step 3: Relate the Selling Prices
Since the selling price of the third person (C) is given as Rs. 250:
\[ SP_C = 250 \]
Using the formula for \( SP_C \):
\[ \frac{5}{4}CP_C = 250 \]
To find \( CP_C \):
\[ CP_C = 250 \times \frac{4}{5} = 200 \]

### Step 4: Find the Selling Price for B
Now, we can find the selling price for B using \( CP_C \):
\[ SP_B = CP_C + \text{Gain on CP_C} = CP_C + \frac{1}{4}CP_C = \frac{5}{4}CP_C \]
Substituting \( CP_C = 200 \):
\[ SP_B = \frac{5}{4} \times 200 = 250 \]

### Step 5: Find the Cost Price for B
Now we can find \( CP_B \):
\[ SP_B = 250 \implies \frac{5}{4}CP_B = 250 \]
Thus,
\[ CP_B = 250 \times \frac{4}{5} = 200 \]

### Step 6: Find the Selling Price for A
Now, we can find the selling price for A using \( CP_B \):
\[ SP_A = CP_B + \text{Gain on CP_B} = CP_B + \frac{1}{4}CP_B = \frac{5}{4}CP_B \]
Substituting \( CP_B = 200 \):
\[ SP_A = \frac{5}{4} \times 200 = 250 \]

### Step 7: Find the Cost Price for A
Now we can find \( CP_A \):
\[ SP_A = 250 \implies \frac{5}{4}CP_A = 250 \]
Thus,
\[ CP_A = 250 \times \frac{4}{5} = 200 \]

### Final Step: Conclusion
The cost price for the first person (A) is Rs. 128.