A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%.

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 .