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The reduction of Rs.12 in the selling price of an article will changes 5% gain into 2(1/2)% loss. The cost price of the article is
The Cost Price of the article is approximately Rs. 160.
To solve this problem, we’ll use the concept of cost price, selling price, and profit/loss percentage.
Let’s denote:
- CP: Cost Price
- SP: Selling Price
Given:
- A reduction of Rs. 12 in the selling price.
- This reduction changes a 5% gain into a 2(1/2)% loss.
We know that:
Gain = Selling Price – Cost Price Loss = Cost Price – Selling Price
Also, we can calculate the percentage change as:
Percentage change = [(Change in value) / (Original value)] * 100
Given that a 5% gain changes to a 2(1/2)% loss with a reduction of Rs. 12 in the selling price, we can set up the equation as follows:
5% Gain – 12 = 2(1/2)% Loss
Converting percentages to decimals: 0.05(Gain) – 12 = -0.025(Loss)
Now, let’s solve for the Cost Price (CP).
-
Find the original Selling Price (SP): Since 5% gain means the selling price is 105% of the cost price, SP = CP + 0.05 * CP = 1.05 * CP
-
Find the reduced Selling Price (SP – Rs. 12): SP – Rs. 12 = 1.05 * CP – 12
-
Now, equate the above with 2(1/2)% loss: 1.05 * CP – 12 = 0.975 * CP
Let’s solve for CP:
1.05 * CP – 0.975 * CP = 12 0.075 * CP = 12 CP = 12 / 0.075 CP ≈ 160
So, the Cost Price of the article is approximately Rs. 160.
Cost Price and Selling Price
Cost price (CP) refers to the price at which a product is purchased or manufactured. It includes all the expenses incurred in the production or acquisition of the product, such as raw material costs, labor costs, overhead costs, etc.
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Selling price (SP) is the price at which a product is sold to the customer. It is the amount that the customer pays to acquire the product.
The profit or loss incurred in a transaction can be calculated using the formula:
Profit = Selling Price – Cost Price
Loss = Cost Price – Selling Price
If the selling price is greater than the cost price, it results in a profit. If the selling price is less than the cost price, it results in a loss.
For example:
Let’s say you buy a product for $50 (cost price) and sell it for $70 (selling price).
Profit = $70 – $50 = $20
In this case, you make a profit of $20.
If you sell the same product for $40:
Loss = $50 – $40 = $10
In this case, you incur a loss of $10.
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Source: Math Hello Kitty
Categories: Math
