# The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

A. 15
B. 16
C. 18
D. 20

### View Solution

The correct answer is x=16 units.
Step by Step Solution

We have 3 elements here cost price (CP), selling price (SP), and profit percentage (Profit%).
So the equations relating them are:

Profit = SP-CP (for loss its CP-SP)

Profit% =\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

Since we don’t know the cost of the article it is ok to assume a value initially.

Let the Cost Price of each article = 1 unit.
Cost Price of 20 articles = 20 units
Selling Price of x articles=CP of 20 articles ⇒ 20 units
Selling Price of 1 article = 20/x

using formula Profit% for 1 article as profit% is a constant for each article.

Profit% =\frac{\text { (selling price – cost price) }}{\text { cost price }} \times 100

25 =\frac{\text { (20-x) }}{\text { x }} \times 100

\frac{25x}{100}\ =\ 20\ -x

\frac{x}{4}\ =\ 20\ -x

x\ =\ 4\left(20\ -x\right)

x\ =\ 80\ -4x

5x\ =\ 80

x\ =\ \frac{80}{5}

x=16

The value of X is 16 units.
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