A man bought two old scooters for Rs. $18000$. By selling one at a profit of $25\%$ and the other at a loss of $20\%$, he neither gains nor loses. Find the cost price of each scooter.

Let the cost price of the first scooter be x, so the second scooter costs 18000 - x. Using the condition for no profit and no loss, 25% of x equals 20% of (18000 - x), which gives 0.25x = 3600 - 0.20x. Solving this linear equation yields 0.45x = 3600, so x = 8000. The cost prices of the two scooters are Rs. 8000 and Rs. 10000.

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