A shopkeeper markes his goods at 40% above the cost price but allows a discount of 5%
for cash payment to his customers . What actual profit does he make , if he receives Rs. 1064
after paying the discount
original cost price -----
selling price = (1.4)(.95)x
1.4(.95)x = 1064
x = 1064/(1.4(.95)) = 800
profit = 1064-800 = 264
check:
first markup = 1.4(800) = 1120
discount of 5% leaves .95(1120) = 1064
264
To find the actual profit made by the shopkeeper, we need to determine the cost price of the goods first.
Let's assume the cost price of the goods is x.
The shopkeeper marks his goods at 40% above the cost price, which means he sells them at 140% of the cost price. So, the selling price (after discount) becomes:
140% of x - 5% of (140% of x)
Now, let's simplify this equation step by step:
Step 1: Calculate the discount amount:
5% of (140% of x) = (5/100) * (140/100) * x = (7/100) * x
Step 2: Calculate the selling price:
140% of x - (7/100) * x = (140/100) * x - (7/100) * x = (133/100) * x
Given that the selling price is Rs. 1064, we can set up the following equation:
(133/100) * x = 1064
To isolate x (the cost price), we can divide both sides by (133/100):
x = (1064 * 100) / 133
x = 800
Therefore, the cost price of the goods is Rs. 800.
Now, let's calculate the profit made by the shopkeeper:
Profit = Selling price - Cost price
Profit = Rs. 1064 - Rs. 800
Profit = Rs. 264
Hence, the shopkeeper makes a profit of Rs. 264.