Mohan bought two old scooters for Rs. 22000. By selling one at a profit of 10% and the other at a loss of 12%, he neither gains nor loses. The cost prices of the dearer of the two scooters isa)Rs. 12,000b)Rs. 10,000c)Rs. 15,000d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
- Mohan bought two old scooters for Rs. 22000.
- He sold one scooter at a profit of 10%.
- He sold the other scooter at a loss of 12%.
- He neither gains nor loses.

To find:
The cost price of the dearer scooter.

Solution:

Let's assume the cost price of the dearer scooter as 'x' and the cost price of the other scooter as 'y'.

Step 1: Setting up equations
- Mohan bought two old scooters for Rs. 22000, so we can write the equation as:
x + y = 22000

- He sold one scooter at a profit of 10%, so the selling price of the first scooter can be written as:
(1 + 10/100)x = 1.1x

- He sold the other scooter at a loss of 12%, so the selling price of the second scooter can be written as:
(1 - 12/100)y = 0.88y

- Mohan neither gains nor loses, so the total selling price of both the scooters should be equal to their total cost price, which can be written as:
1.1x + 0.88y = x + y

Step 2: Simplifying the equations
- We can simplify the equation x + y = 22000 to y = 22000 - x.

- We can simplify the equation 1.1x + 0.88y = x + y as 0.1x - 0.12y = 0.

Step 3: Solving the equations
Substituting the value of y from the first equation into the second equation, we get:
0.1x - 0.12(22000 - x) = 0
0.1x - 0.12(22000) + 0.12x = 0
0.1x - 2640 + 0.12x = 0
0.22x - 2640 = 0
0.22x = 2640
x = 2640 / 0.22
x = 12000

So, the cost price of the dearer scooter is Rs. 12000.

Conclusion:
Therefore, the correct answer is option 'B': Rs. 10,000.

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