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5 pencils and 7 pens together cost Rs.50, whereas 7 pencils and 5 pens together cost Rs.46. Find the costs of one pencil and one pen.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

5 pencils and 7 pens together cost Rs.50, whereas 7 pencils and 5 pens together cost Rs.46. Find the costs of one pencil and one pen.

The cost price refers to the price at which the product is acquired or manufactured, while the selling price is the price at which it is sold to customers, taking into account the cost price and the desired profit margin. To find the costs of one pencil and one pen one must solve both the equations either by substitution or elimination method. Hence, the cost of one pencil is Rs. 3 and the cost of one pen is Rs. 5.

Table of content

1. Cost Price And Selling Price
2. 5 pencils and 7 pens together cost Rs.50, whereas 7 pencils and 5 pens together cost Rs.46. Find the costs of one pencil and one pen.

Cost Price And Selling Price

Cost price (CP) refers to the price at which a product or item is purchased or produced. It is the cost incurred by a seller to acquire or manufacture the product. Selling price (SP) refers to the price at which a product or item is sold to customers or buyers. It is the price at which the seller offers the product for sale in the market.

In simple terms, the cost price is the amount paid by the seller, while the selling price is the amount received by the seller for selling the product. The selling price is generally higher than the cost price, as it includes the cost price plus a profit margin. The difference between the selling price and the cost price is known as the profit if the selling price is higher than the cost price. Conversely, if the selling price is lower than the cost price, the difference is referred to as a loss.

Profit = Selling Price – Cost Price

Loss = Cost Price – Selling Price

Solution

Let’s denote the cost of one pencil as x and the cost of one pen as y in rupees.

From the given information, we can form two equations:

Equation 1: 5x + 7y = 50

Equation 2: 7x + 5y = 46

Solve Equation 1 for x:

5x = 50 – 7y

x = (50 – 7y) / 5

Substitute x in Equation 2:

7((50 – 7y) / 5) + 5y = 46

Multiply through by 5 to eliminate the fraction:

7(50 – 7y) + 25y = 230

350 – 49y + 25y = 230

-24y = -120

y = 5

Substitute y = 5 back into Equation 1 to find x:

5x + 7(5) = 50

5x + 35 = 50

5x = 15

x = 3

Therefore, the cost of one pencil is Rs. 3 and the cost of one pen is Rs. 5.

Summary