Question

a person marks his goods x% above the cost price and allows a discount of 10% on the marked price. if his profit is 20% then the value of x will be:

Answer 1

To find the value of x, we can use the given information about the profit, cost price, and selling price. By setting up an equation and solving for x, we can determine its value. Assumptions can also be made for the cost price to find the value of x. In this case, the value of x is approximately 33.33.

Step-by-step explanation:

To find the value of x, we need to follow these steps:

1. Let the cost price of the goods be CP.
2. The person marks the goods x% above the cost price, so the marked price is (100 + x)% of the cost price.
3. Now, the person allows a discount of 10% on the marked price, so the selling price is 90% of the marked price.
4. Given that the profit is 20%, we can use the formula: Profit = Selling Price - Cost Price
5. Substituting the values, we get: 20% of CP = (90% of (100 + x)% of CP) - CP
6. Simplifying the equation, we get: 20% of CP = 90% of (100 + x)% of CP - CP
7. Further simplifying, we get: (20/100) * CP = (90/100) * (100 + x)/100 * CP - CP
8. Cross multiplying and solving for x, we get: 20 * 100 = 90 * (100 + x) - 100 * CP
9. Now, we can substitute the value of CP into the equation or assume a value for CP to find the value of x.
10. For example, let's assume CP = $100.
11. Substituting this value into the equation and solving for x, we get 2000 = 90 * (100 + x) - 100 * 100
12. Simplifying, we get 2000 = 90 * (100 + x) - 10000
13. Moving the terms around, we get 90 * (100 + x) = 2000 + 10000
14. Simplifying, we get 90 * (100 + x) = 12000
15. Dividing both sides by 90, we get 100 + x = 12000/90
16. Simplifying, we get 100 + x = 133.33
17. Subtracting 100 from both sides, we get x = 33.33

Therefore, the value of x is approximately 33.33.