Question

A man sells two horses for Rs. 4000 each, neither losing nor gaining in the deal. If he sold one horse at a gain of 25%, the other horse is sold at a loss of:
(a) $33\dfrac{1}{3}\%$
(b) $16\dfrac{2}{3}\%$
(c) 50%
(d) 47%

Answer 1

Hint: Let the cost price of one of the horses be Rs. x and that of the other be Rs. y. It is given that he sold the first horse for 25% profit at the cost of Rs. 4000, so, x added with 25% of x is 4000. So, using this, find the value of x. Once you get x, find y using the fact that the total cost price is Rs. 8000. Once you get y, find the loss and convert it to percent with respect to y to get the answer.

Complete step-by-step answer:
To start the solution to the above question, we let the cost price of the one of the horses be Rs. x and that of the other be Rs. y.
It is given that he sold the first horse for 25% profit at the cost of Rs. 4000, so, x added with 25% of x is 4000. So, if we represent this mathematically, we get
$x+\dfrac{25}{100}\times x=4000$
$\Rightarrow \dfrac{125}{100}x=4000$
$\Rightarrow x=4000\times \dfrac{4}{5}=3200$
So, the cost price of the first horse is Rs. 3200. It is given that the cost price and selling price of the two horses together are equal. So, the SP of the 2 horses together is $2\times 4000=8000$ and if we subtract the cost of the first horse from it we get the cost price of the other horse, i.e., y.
$y=8000-3200=4800$
Also, the selling price of the second horse is also Rs. 4000, so, the net loss in the second horse is 4800-4000=Rs. 800.
Now let us concert the loss to percentage by dividing it by CP of the second horse and multiplying by 100.
$loss=\dfrac{800}{4800}\times 100=\dfrac{100}{6}=\dfrac{50}{3}$
Now, to convert it to a mixed fraction we will use the fact that when 50 is divided by 3 it gives 16 as the quotient and 2 as the remainder.
$loss=\dfrac{50}{3}=16\dfrac{2}{3}\%$
Hence, the answer to the above question is option (b).

Note: The key to the above question is to interpret it properly that the cost price of the two horses are different and the average of their selling price is given in the question. The other important thing is to always try to keep the fractions in simple form, this reduces the chance of making errors and if needed convert the fraction to mixed form in the last steps as we did in the above question.