Maths question from Panchayat Secretary (VLW) exam, 2025 by JKSSB
A cycle has a marked price of Rs. 15,000. It is sold at a discount of p%. Even after this discount, a profit of p% is earned. Find the value of p if cost price of cycle is Rs. 10,000.
Last updated Jun 13, 2026
Correct Answer:
Option B —
20%
Step-by-Step Explanation
We can solve this problem by finding the selling price in two different ways: first through the cost price and profit, and second through the marked price and discount.
Step 1: Express the selling price using the cost price and profit
The cost price of the cycle is 10,000 rupees.
The profit earned is p percent.
To find the selling price, we take the cost price and add the profit amount. The profit amount is found by multiplying the cost price (10,000) by p percent (p divided by 100), which simplifies to 100 times p.
Therefore, the selling price equals 10,000 plus 100 times p.
Step 2: Express the selling price using the marked price and discount
The marked price of the cycle is 15,000 rupees.
The discount given is p percent.
To find the selling price this way, we take the marked price and subtract the discount amount. The discount amount is found by multiplying the marked price (15,000) by p percent (p divided by 100), which simplifies to 150 times p.
Therefore, the selling price also equals 15,000 minus 150 times p.
Step 3: Combine and solve for p
Since both expressions represent the exact same selling price, they must be equal to each other:
10,000 plus 100 times p equals 15,000 minus 150 times p.
Now, we bring all the terms with p to one side by adding 150 times p to both sides:
10,000 plus 250 times p equals 15,000.
Next, we subtract 10,000 from both sides to isolate the p term:
250 times p equals 5,000.
Finally, we divide 5,000 by 250 to find the value of p:
p equals 20.
Thus, the value of p is 20%.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
