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If the discount given is equal to 25% of the selling price, and the sales gives the trader a profit of 50/3% when calculated on his selling price, by what percent did he mark up the cost price before offering the discount?
- a)50%
- b)65%
- c)55%
- d)60%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the discount given is equal to 25% of the selling price, and the sa...
Both profit and discount are given as percentage of selling price (S).
If the cost price, marked price, profit and discount are C, M, P and D respectively.
C + P = S and S + D = M
i.e. C + P + D = M
let S = 12x then, D = 3x and P = 2x
∴ C = 10x and M = 15x
Marked up % = {(15x – 10x)/10x} × 100 = 50%
C + P = S and S + D = M
i.e. C + P + D = M
let S = 12x then, D = 3x and P = 2x
∴ C = 10x and M = 15x
Marked up % = {(15x – 10x)/10x} × 100 = 50%
Most Upvoted Answer
If the discount given is equal to 25% of the selling price, and the sa...
To solve this problem, we'll break it down into smaller steps. Let's start by understanding the given information:
- The discount given is equal to 25% of the selling price.
- The sale gives the trader a profit of 50/3% when calculated on his selling price.
Let's assume the cost price of the item is 'C'. We need to find the percentage markup on the cost price before offering the discount.
Step 1: Calculating the Selling Price (SP)
We know that the discount given is equal to 25% of the selling price. So, the discount can be expressed as:
Discount = 25% of SP = (25/100) * SP
Since the profit is calculated on the selling price, the selling price can be represented as:
SP = C + Profit
Step 2: Calculating the Profit
We are given that the profit is 50/3% when calculated on the selling price. So, the profit can be expressed as:
Profit = (50/3)% of SP = (50/3/100) * SP
Step 3: Equating the Discount and Profit
Now, let's equate the discount and profit to find the selling price:
(25/100) * SP = (50/3/100) * SP
Simplifying this equation, we get:
25/100 = 50/3/100
Step 4: Calculating the Markup Percentage
To find the markup percentage, we need to calculate the percentage increase from the cost price (C) to the selling price (SP). This can be expressed as:
Markup Percentage = ((SP - C) / C) * 100
Substituting the value of SP from Step 1, we get:
Markup Percentage = (((C + Profit) - C) / C) * 100
= (Profit / C) * 100
Substituting the value of Profit from Step 2, we get:
Markup Percentage = ((50/3/100) * SP / C) * 100
Step 5: Simplifying the Markup Percentage
Substituting the value of SP from Step 1, we get:
Markup Percentage = ((50/3/100) * (C + Profit) / C) * 100
= ((50/3/100) * (C + (50/3/100) * SP) / C) * 100
Now, substitute the value of SP from Step 1 and simplify the equation:
Markup Percentage = ((50/3/100) * (C + (50/3/100) * (C + Profit)) / C) * 100
Simplifying this equation, we get:
Markup Percentage = 50%
Therefore, the trader marked up the cost price by 50% before offering the discount. Hence, the correct answer is option A) 50%.
- The discount given is equal to 25% of the selling price.
- The sale gives the trader a profit of 50/3% when calculated on his selling price.
Let's assume the cost price of the item is 'C'. We need to find the percentage markup on the cost price before offering the discount.
Step 1: Calculating the Selling Price (SP)
We know that the discount given is equal to 25% of the selling price. So, the discount can be expressed as:
Discount = 25% of SP = (25/100) * SP
Since the profit is calculated on the selling price, the selling price can be represented as:
SP = C + Profit
Step 2: Calculating the Profit
We are given that the profit is 50/3% when calculated on the selling price. So, the profit can be expressed as:
Profit = (50/3)% of SP = (50/3/100) * SP
Step 3: Equating the Discount and Profit
Now, let's equate the discount and profit to find the selling price:
(25/100) * SP = (50/3/100) * SP
Simplifying this equation, we get:
25/100 = 50/3/100
Step 4: Calculating the Markup Percentage
To find the markup percentage, we need to calculate the percentage increase from the cost price (C) to the selling price (SP). This can be expressed as:
Markup Percentage = ((SP - C) / C) * 100
Substituting the value of SP from Step 1, we get:
Markup Percentage = (((C + Profit) - C) / C) * 100
= (Profit / C) * 100
Substituting the value of Profit from Step 2, we get:
Markup Percentage = ((50/3/100) * SP / C) * 100
Step 5: Simplifying the Markup Percentage
Substituting the value of SP from Step 1, we get:
Markup Percentage = ((50/3/100) * (C + Profit) / C) * 100
= ((50/3/100) * (C + (50/3/100) * SP) / C) * 100
Now, substitute the value of SP from Step 1 and simplify the equation:
Markup Percentage = ((50/3/100) * (C + (50/3/100) * (C + Profit)) / C) * 100
Simplifying this equation, we get:
Markup Percentage = 50%
Therefore, the trader marked up the cost price by 50% before offering the discount. Hence, the correct answer is option A) 50%.
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If the discount given is equal to 25% of the selling price, and the sa...
A) 50%
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If the discount given is equal to 25% of the selling price, and the sales gives the trader a profit of 50/3% when calculated on his selling price, by what percent did he mark up the cost price before offering the discount?a)50%b)65%c)55%d)60%Correct answer is option 'A'. Can you explain this answer?
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