A shopkeeper organizes sale on Friday, offering a discount of 23% on all items. Still, he makes a profit of 10% only. By how much percentage CP was lower than MP?
Question
A shopkeeper organizes sale on Friday, offering a discount of 23% on all items. Still, he makes a profit of 10% only. By how much percentage CP was lower than MP?
Solution
To solve this problem, we need to understand the relationship between the cost price (CP), the marked price (MP), and the discount offered.
Step 1: Let's assume the cost price (CP) of the item is $100.
Step 2: The shopkeeper makes a profit of 10%, so the selling price (SP) of the item is 100 is $110).
Step 3: The shopkeeper offers a discount of 23% on all items. This means the marked price (MP) is higher than the selling price (SP).
Step 4: If we let x be the marked price (MP), then the selling price (SP) is 77% of the marked price (MP), because the discount is 23%. So, we can write the equation 0.77x = $110.
Step 5: Solving this equation for x gives us x = 142.86. This is the marked price (MP).
Step 6: To find out by how much percentage the cost price (CP) was lower than the marked price (MP), we subtract the cost price (CP) from the marked price (MP), divide by the marked price (MP), and multiply by 100.
So, the percentage by which the cost price (CP) was lower than the marked price (MP) is ((100) / $142.86) * 100 = approximately 30%.
So, the cost price was approximately 30% lower than the marked price.
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