a man bought a horse and a carriage for rs. 3000. he sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. find the cost of the horse.
To find the cost of the horse, we can start by calculating the selling price of both the horse and the carriage after the respective gains and losses.
Let’s assume the cost of the horse is “x” rupees.
According to the given information, the horse was sold at a 20% profit. Therefore, the selling price of the horse would be x + (20% of x) = x + 0.2x = 1.2x rupees.
Similarly, the carriage was sold at a 10% loss. So, the selling price of the carriage would be (3000 - x) - (10% of (3000 - x)) = 3000 - x - 0.1(3000 - x) = 3000 - x - 0.1x + 0.1x = 3000 - 0.9x rupees.
Now, let’s calculate the overall gain percentage.
The man gained 2% on the whole transaction, so the overall selling price would be (1 + 2/100) multiplied by the total cost, which is 3000 rupees.
Therefore, (1 + 2/100) * 3000 = 1.02 * 3000 = 3060 rupees.
To find the cost of the horse, we can set up an equation:
1.2x + (3000 - 0.9x) = 3060
Solving this equation will give us the value of x, which is the cost of the horse.
1.2x + 3000 - 0.9x = 3060
0.3x + 3000 = 3060
0.3x = 60
x = 60 / 0.3
x = 200
Therefore, the cost of the horse is 2000 rupees.