A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%.
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.
Solution:
Given,
Gain on one cycle $=$ Rs. 360
Gain $=20 \%$
Gain $\%=\frac{\text { Gain }}{\mathrm{CP}} \times 100$
$20=\frac{360}{\mathrm{CP}} \times 100$
$\mathrm{CP}=$ Rs. 1800
$\mathrm{SP}=\frac{100+\text { Gain } \%}{100} \times \mathrm{CP}$
$\mathrm{SP}=\frac{120}{100} \times 1800=$ Rs. 2160
$\mathrm{SP}=$ Rs. 2160
Discount $=20 \%$
$\mathrm{MP}=\frac{100 \times \mathrm{SP}}{100-\text { Discount } \%}$
$\mathrm{MP}=\frac{100 \times 2160}{80}=$ Rs. 2700
Hence, the MP of one cycle is Rs. 2700 .