# 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

## 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**

## 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.

5 pencils and 7 pens together cost Rs.50, whereas 7 pencils and 5 pens together cost Rs.46. The costs of one pencil and one pen are Rs. 3 and Rs. 5 respectively.

**Related Questions**

- Balance the following chemical equation- HNO3 + Ca(OH)2 → Ca(NO3)2 + H2O
- Find the probability of selecting a vowel from word ‘MATHEMATICS’
- What is the difference between Atleast and Atmost in Probability?
- Four boys and three girls stand in a queue for an interview, the probability that they will be in alternate positions is.
- The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey?
- A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.