Question

A man bought a horse and a carriage for 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.
A. 1000
B. 1200
C. 1500
D. 1650

Answer 1

Hint:- We can assume the cost of horse as variable x and then we can find the total selling cost of horse and carriage and on comparing that with the 3000 + 2% of 3000 we will get the value of x.

Complete step-by-step answer:
Let the cost of horse will be Rs. x
So, the cost of the carriage will be Rs. (3000 – x).
Now as we know that horse is sold at the 20% gain.
So, we can find the gain amount by using the percentage formula.
As we know that according to percentage formula B% of A will be \[\dfrac{B}{{100}} \times A\]
So, the 20% of the cost of horse (i.e. x) will be \[\dfrac{{20}}{{100}} \times x = \dfrac{x}{5}\]
So, the horse will be sold by the man at a price of x + \[\dfrac{x}{5}\] = Rs. \[\dfrac{{6x}}{5}\]
Now, we had to find the selling price of carriage.
So, the 10% of the cost of carriage (i.e. 3000 – x) will be \[\dfrac{{10}}{{100}} \times \left( {3000 - x} \right) = \dfrac{{\left( {3000 - x} \right)}}{{10}}\]
Now as the man sold the carriage at the loss of 10%.
So, the selling price of carriage will be (3000 – x) – \[\dfrac{{\left( {3000 - x} \right)}}{{10}}\] = \[\dfrac{{9\left( {3000 - x} \right)}}{{10}}\]
So, the total cost of selling horse and carriage will be \[\dfrac{{6x}}{5} + \dfrac{{9\left( {3000 - x} \right)}}{{10}} = \dfrac{{12x + 27000 - 9x}}{{10}} = \dfrac{{3x + 27000}}{{10}}\] (1)
Now as it is given that the man gains 2% on the whole price.
So, 2% of 3000 will be \[\dfrac{2}{{100}} \times 3000 = 60\]
So, the total selling price will be Rs (3000 + 60) = Rs. 3060
So, now equating equation 1 with 3060.
  \[\dfrac{{3x + 27000}}{{10}}\] = 3060
Cross-multiplying above equation.
3x + 27000 = 30600
Subtracting 27000 from both the sides of the above equation.
3x = 3600
Dividing both sides of the above equation by 3.
x = 1200
So, the cost of the horse will be Rs. 1200.
Hence, the correct option will be B.

Note:- Whenever we come up with this type of then there is also an alternate method to find the selling price directly like if the cost of any article is A and it is sold at a gain percent of B% then the selling price of the article will be \[\dfrac{{\left( {100 + B} \right)}}{{100}} \times A\], and if the article is sold at the loss percent of B% then the selling price of the article will be \[\dfrac{{\left( {100 - B} \right)}}{{100}} \times A\].