Question

A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle.

Answer 1

$$\text{ Given },$$

$$\text{ Gain on one cycle = Rs . }360$$

$$\text{ Gain = 20 \% }$$

$$\text{ Gain \% }=\frac{\text{ Gain }}{CP}\times 100$$

$$20=\frac{360}{CP}\times 100$$

$$CP=Rs.1800$$

$$SP=\frac{100+\text{ Gain \% }}{100}\times CP$$

$$SP=\frac{120}{100}\times 1800=Rs.2160$$

$$\text{ SP = Rs }.2160$$

$$\text{ Discount = 20 \% }$$

$$\text{ MP }=\frac{100\times SP}{100-\text{ Discount \% }}$$

$$\text{ MP }=\frac{100\times 2160}{80}=Rs.2700$$

$$\text{ Hence, the MP of one cycle is Rs }.2700.$$