Question

A merchant loss 8% by selling a cycle for Rs.1288. At what price should he sell it in order to gain 8%.

Answer 1

Hint- If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. In this question, two equations will be formed for the two conditions given which needs to be solved for the selling price of the cycle.

Complete step by step solution:
Substitute Loss%=8% and SP=1288 in the formula $Loss\% = \dfrac{{CP - SP}}{{CP}} \times 100\% $ to determine the cost price of the cycle to the merchant as:

$
  Loss\% = \dfrac{{CP - SP}}{{CP}} \times 100\% \\
  8 = \dfrac{{CP - 1288}}{{CP}} \times 100 \\
  8CP = \left( {CP - 1288} \right)100 \\
  \left( {100 - 8} \right)CP = 128800 \\
  CP = \dfrac{{128800}}{{92}} \\
   = 1400 \\
 $

Hence, the actual cost price of the cycle is Rs.1400.

Now, in other case merchant want to take gain 8%,
So, substitute gain=8% and cost price= Rs. 1400 in the formula $gain\% = \dfrac{{SP - CP}}{{CP}} \times 100\% $ to determine the selling price of the cycle by the merchant as:

 $
  gain\% = \dfrac{{SP - CP}}{{CP}} \times 100\% \\
  8 = \dfrac{{SP - 1400}}{{1400}} \times 100 \\
  8 = \dfrac{{SP - 1400}}{{14}} \\
  8 \times 14 = SP - 1400 \\
  SP = 1400 + 112 \\
   = 1512 \\
 $

Hence, to get a profit of 8%,the merchant should have to sell the cycle at Rs. 1512.

Note: Students usually get confused between the cost price and marked price. Marked price is the normal price of the product without any discount or we can say the price printed on the item while the Cost price is the amount at which the shopkeeper buys the item.