The marked price of the bulb is 60% more than its cost price. A shopkeeper offers a discount of x% on marked price of the bulb while he gets the profit of 36%. Find the value of x? 

By MathHelloKitty

Explore the shopkeeper's strategy: Find the discounted value of a bulb priced 60% higher than its cost price, ensuring a 36% profit.

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The marked price of the bulb is 60% more than its cost price. A shopkeeper offers a discount of x% on marked price of the bulb while he gets the profit of 36%. Find the value of x?

Let’s assume the cost price of the bulb is $C.

According to the given information, the marked price (MP) of the bulb is 60% more than its cost price:

Marked Price (MP) = Cost Price (C) + 60% of Cost Price = C + 0.6C = 1.6C

Now, the shopkeeper offers a discount of x% on the marked price. After the discount, the selling price (SP) of the bulb becomes:

Selling Price (SP) = Marked Price (MP) – Discount = 1.6C – (x/100) * 1.6C = 1.6C(1 – x/100)

Given that the shopkeeper gets a profit of 36%, we can equate the profit to the difference between the selling price and the cost price:

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Profit = Selling Price – Cost Price = SP – C = 0.36C

Now, we can equate this profit to the difference between the selling price and the cost price:

0.36C = 1.6C(1 – x/100) – C

Now, let’s solve for x:

0.36C = 1.6C – (1.6Cx/100) – C

0.36C = 0.6C – (1.6Cx/100)

0.36C – 0.6C = – (1.6Cx/100)

-0.24C = – (1.6Cx/100)

0.24C = (1.6Cx/100)

Multiply both sides by 100:

24C = 1.6Cx

Divide both sides by 1.6C:

15 = x

So, the value of x is 15. Therefore, the shopkeeper offers a discount of 15%.

Profit and Loss in Mathematics

In mathematics, profit and loss are concepts related to business and finance. They are typically expressed in terms of money and represent the financial outcome of a transaction or business operation.

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  1. Profit: Profit is the financial gain realized when the revenue generated from a business activity exceeds the expenses and costs incurred in carrying out that activity. Mathematically, profit can be calculated using the formula:

    Profit = Revenue – Cost

    Where:

    • Revenue is the total income generated from sales or other business activities.
    • Cost includes all expenses incurred in producing goods or services, such as production costs, operating expenses, taxes, and other overheads.

  2. Loss: Loss occurs when the expenses and costs of a business activity exceed the revenue generated from that activity. Mathematically, loss can be calculated using the formula:

    Loss = Cost – Revenue

    Where the terms are the same as defined above for profit.

  3. Profit Percentage: Profit percentage represents the profit earned as a percentage of the cost price (the price at which an item is purchased or produced). It is calculated using the formula:

    Profit Percentage = (Profit / Cost) * 100%

  4. Loss Percentage: Loss percentage represents the loss incurred as a percentage of the cost price. It is calculated using the formula:

    Loss Percentage = (Loss / Cost) * 100%

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These concepts are fundamental in business and finance and are often used to analyze the financial performance of a business, evaluate investment opportunities, and make strategic decisions.

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Source: Math Hello Kitty
Categories: Math