Question

22. When an article is sold for Rs.116, the profit percent is thrice as much as when
it is sold for Rs.92. The cost price of the article is​

Answer 1

Given:

When an article is sold for Rs.116, the profit per cent is thrice as much as when  it is sold for Rs.92

To find:

The cost price of the article

Solution:

Let "x" represent the cost price of the article.

We have the formula as:

$\boxed{\bold{Profit\% = \frac{S.P. - C.P. }{C.P.}\times 100 }}$

So,

When the article is sold for Rs. 116, we have

Profit% = $\frac{116 - x}{x}\times 100$ = $\frac{11600 - 100x}{x}$

and

When the is sold for Rs. 92, we have

Profit% = $\frac{92 - x}{x}\times 100$ = $\frac{9200 - 100x}{x}$

Now, according to the question, we have

[Proift% when the article is sold for Rs. 116] = 3 × [Proift% when the article is sold for Rs. 92]

⇒ $\frac{11600 - 100x}{x} = 3 \times \frac{9200 - 100x}{x}$

⇒ $11600 - 100x = 3 \times (9200 - 100x)$

⇒ $11600 - 100x = 27600 - 300x$

⇒ $300x - 100x = 27600 - 11600$

⇒ $200x = 16000$

⇒ $x = \frac{16000}{200}$

⇒ $\bold{x = 80}$

Thus, the cost price of the article is Rs. 80.

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