A shopkeeper marks up price of his product by 40%.if he increases the discount from 5 to 10 %,the product would decreases by rs14.how much profit would he earn,if he gives a discount of 20% as marked price?
Evaluate each expression using the Order of Operations.
To find the profit, we need to consider the original price of the product, the final selling price after all the discounts, and the cost price after the 40% markup.
Let's assume the cost price (CP) of the product is x.
Given that the shopkeeper marks up the price by 40%, the selling price (SP) becomes:
SP = CP + 0.4CP
SP = 1.4CP
Now, let's calculate the final selling price after all the discounts.
1. With a discount of 5%:
Discounted Price = SP - (0.05 * SP)
Discounted Price = 1.4CP - (0.05 * 1.4CP)
Discounted Price = 1.4CP - 0.07CP
Discounted Price = 1.33CP
2. With a discount of 10%:
Discounted Price = SP - (0.1 * SP)
Discounted Price = 1.4CP - (0.1 * 1.4CP)
Discounted Price = 1.4CP - 0.14CP
Discounted Price = 1.26CP
Given that the product decreases by Rs. 14 when the discount increases from 5% to 10%, we can set up the following equation:
1.33CP - 1.26CP = 14
0.07CP = 14
CP = 14 / 0.07
CP = 200
Therefore, the cost price of the product is Rs. 200.
Now, let's calculate the selling price with a discount of 20% as marked price:
Discounted Price = SP - (0.2 * SP)
Discounted Price = 1.4CP - (0.2 * 1.4CP)
Discounted Price = 1.4CP - 0.28CP
Discounted Price = 1.12CP
Selling Price = 1.12 * 200 = Rs. 224
Profit = Selling Price - Cost Price
Profit = 224 - 200
Profit = Rs. 24
Therefore, the shopkeeper would earn a profit of Rs. 24 if he gives a discount of 20% as the marked price.
To find the profit earned by the shopkeeper, we need to calculate the original cost price and the selling price after giving a discount of 20%.
Let's start by considering the original marked price (before giving any discount) of the product as 'x' rupees.
Given that the shopkeeper marks up the product price by 40%, the selling price before discount can be calculated as:
Selling Price = Marked Price + (Marked Price * Markup Percentage)
= x + (x * 40/100)
= x + 0.4x
= 1.4x
Next, we are given that if the shopkeeper increases the discount from 5% to 10%, the price of the product would decrease by 14 rupees.
This means that the difference in selling prices before and after increasing the discount is 14 rupees.
So, 1.4x - (0.9 * 1.4x) = 14
Solving the above equation, we get:
0.5 * 1.4x = 14
0.7x = 14
x = 14 / 0.7
x = 20
Now we know that the original marked price of the product is 20 rupees.
If the shopkeeper gives a discount of 20% on this marked price, the selling price will be calculated as:
Selling Price = Marked Price - (Marked Price * Discount Percentage)
= 20 - (20 * 20/100)
= 20 - 4
= 16 rupees
To find the profit earned, we need to subtract the cost price from the selling price.
Since the shopkeeper always earns profit, the cost price will be less than the selling price.
Given that the selling price is 16 rupees, we can calculate the cost price as follows:
Cost Price = Selling Price / (1 + Profit Percentage)
= 16 / (1 + 20/100)
= 16 / (1 + 0.2)
= 16 / 1.2
= 13.33 rupees (approx.)
Therefore, the profit earned by the shopkeeper when giving a discount of 20% is:
Profit = Selling Price - Cost Price
= 16 - 13.33
= 2.67 rupees (approx.)
Hence, the shopkeeper would earn a profit of approximately 2.67 rupees when giving a discount of 20% based on the marked price of 20 rupees.
If the original price was x, then
1.4x*.95 - 1.4x*.90 = 14
x = 200
1.4*200 - 1.4*200*.8 = 224
so, the profit would be 24, or 12%.