A tricycle is sold at a gain of `15%`. Had it been sold for `₹ 108` more, the profit would have been `20%`. Find its cost price.

Options

A. `2160`
B. `2000`
C. `2100`
D. `2560`

Answer

To find the cost price of the tricycle, we can follow these steps:

### Step 1: Define the Cost Price
Let the cost price (CP) of the tricycle be \( x \).

### Step 2: Calculate Selling Price at 15% Gain
The selling price (SP) when sold at a gain of 15% can be calculated using the formula:
\[ SP = CP + \text{Gain} \]
Where Gain = \( 15\% \) of CP = \( \frac{15}{100} \times x \).

Thus, the selling price at 15% gain is:
\[ SP_1 = x + \frac{15}{100} \times x = \frac{115}{100} \times x = 1.15x \]

### Step 3: Calculate Selling Price at 20% Gain
If the tricycle is sold for ₹108 more, the new selling price would be:
\[ SP_2 = SP_1 + 108 = 1.15x + 108 \]
The selling price at a gain of 20% is:
\[ SP_2 = CP + \text{Gain} \]
Where Gain = \( 20\% \) of CP = \( \frac{20}{100} \times x \).

Thus, the selling price at 20% gain is:
\[ SP_2 = x + \frac{20}{100} \times x = \frac{120}{100} \times x = 1.2x \]

### Step 4: Set Up the Equation
Now, we can set the two expressions for \( SP_2 \) equal to each other:
\[ 1.15x + 108 = 1.2x \]

### Step 5: Solve for x
Rearranging the equation gives:
\[ 1.2x - 1.15x = 108 \]
\[ 0.05x = 108 \]
Now, divide both sides by 0.05 to find \( x \):
\[ x = \frac{108}{0.05} = 108 \times 20 = 2160 \]

### Conclusion
The cost price of the tricycle is \( ₹ 2160 \).

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