The cost price of 36 articles is the same as the selling price of N articles. If the profit is 20%, then the value of N is:

The correct answer is 30.

Step-by-step explanation:

Let the cost price (CP) of 1 article be 1 unit.

Therefore, the cost price of 36 articles is:

$\text{CP of 36 articles}=36$

According to the question, the cost price of 36 articles is equal to the selling price (SP) of N articles:

$\text{SP of N articles}=36$

The cost price of N articles is:

$\text{CP of N articles}=N$

The profit made on selling N articles can be expressed as:

$\text{Profit}=\text{SP of N articles}-\text{CP of N articles}$

$\text{Profit}=36-N$

We are given that the profit percentage is 20%. The formula for profit percentage is:

$\text{Profit \%}=\left(\frac{\text{Profit}}{\text{CP of N articles}}\right)\times 100$

Substituting the values into the formula:

$20=\left(\frac{36-N}{N}\right)\times 100$

Simplify by dividing both sides by 100:

$\frac{20}{100}=\frac{36-N}{N}$

$\frac{1}{5}=\frac{36-N}{N}$

Cross-multiply to solve for N:

$1\times N=5\times \left(36-N\right)$

$N=180-5N$

Add 5N to both sides of the equation:

$N+5N=180$

$6N=180$

Divide by 6:

$N=\frac{180}{6}$

$N=30$

Thus, the value of N is 30.