# Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is

A. 33%
B. 33 \frac{1}{3} \%
C. 35%
D. 44%

Step by step Solution:

According to the problem statement,
⇒ The cost price of 6 articles is 5, then the cost price of 1 article would be RS \cdot \frac{5}{6}

⇒ The selling price of 5 articles is 6, then the selling price of 1 article would be RS \cdot \frac{6}{5}

Now Gain % Formula is,

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

By putting Values, it will be

\frac{\left(\frac{6}{5}-\frac{5}{6}\right)}{\left(\frac{5}{6}\right)} \times 100

Taking LCM of Cost price and Selling price,

\frac{\left(\frac{36-25}{30}\right)}{\left(\frac{5}{6}\right)} \times 100

\frac{\left(\frac{11}{30}\right)}{\left(\frac{5}{6}\right)} \times 100

\left(\frac{11}{30}\right) \times\left(\frac{6}{5}\right) \times 100

\begin{array}{l}\frac{11\ \times\ 6}{30\ \times5}\ \times100\ ⇒\frac{66}{150}\ \times\ 100\ ⇒\frac{6600}{150}\ =\ 44\ \%\end{array}

Alternate Solution:

You can calculate gain % by simple method;
let’s suppose we have bought the number of articles, take LCM of 6 and 5, it is 30.
Now, as we know the number of articles bought, we can calculate Cost price and selling price.

Cost price =R s .\left(\frac{5}{6} \times 30\right)=R s .25

Selling Price =R s .\left(\frac{6}{5} \times 30\right)=R s .36

Now, by putting values in the Gain% formula

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

Gain% =\frac{\text { (RS. 36 – RS. 25) }}{\text { RS. 25 }} \times 100

Gain% =\frac{\text { (RS. 11) }}{\text { RS. 25 }} \times 100

Gain% = 44%
Thus, Gain% is 44%.
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