A second-hand car was sold at a profit of $25\%$. Had it been sold for ₹$26,875$ less, the profit would have been $12\%$. What is the cost price (in ₹, to the nearest integer) of the car?

Let the cost price ($\text{CP}$) of the car be $100\%$.Initial Selling Price (${\text{SP}}_1$) at $25\%$ profit = $125\%$ of $\text{CP}$ New Selling Price (${\text{SP}}_2$) at $12\%$ profit = $112\%$ of $\text{CP}$ The difference between the two selling prices is given as ₹$26,875$:
$${\text{SP}}_1-{\text{SP}}_2=125\%-112\%=13\%\text{ of CP}$$
Thus:
$$13\%\text{ of CP}=26875$$
$$\frac{13}{100}\times \text{CP}=26875$$
$$\text{CP}=\frac{26875\times 100}{13}$$
Let's divide $26875$ by $13$:
$$26875÷13=\mathrm{2067.30769...}$$
Multiply by $100$:
$$\text{CP}=\mathrm{206730.769...}$$
Rounding to the nearest integer gives ₹$2,06,731$.