At a village trade fair, a man buys a horse and a camel for a total amount of $\text{₹}5,125$. He sold the horse at a profit of $25\%$ and the camel at a loss of $20\%$. If he had sold both the animals at the same price, then the cost price of the cheaper animal was:

Let the cost price of the horse be $H$ and the cost price of the camel be $C$.
Given that the total cost price is:

$$H+C=5,125$$

The selling price of the horse at $25\%$ profit is:

$${\text{SP}}_H=1.25\times H=\frac{5}{4}H$$

The selling price of the camel at $20\%$ loss is:

$${\text{SP}}_C=0.80\times C=\frac{4}{5}C$$

Since both selling prices are equal:

$$\frac{5}{4}H=\frac{4}{5}C⟹\frac{H}{C}=\frac{4\times 4}{5\times 5}=\frac{16}{25}$$

Let $H=16k$ and $C=25k$.
Summing their cost prices:

$$16k+25k=5,125⟹41k=5,125$$

$$k=\frac{5,125}{41}=125$$

The cheaper animal is the horse with a cost price of $16k$:

$$\text{CP of Horse}=16\times 125=\text{₹}2,000$$