Question

Ravish bought 100 articles for Rs. 4000. He sold 20 of them at a gain of 5%. At what gain percent must sell the remaining articles so as to gain 20% on the whole?

Answer 1

Hint: First find the selling price of 20 articles. After that find the selling price of all articles. Then, subtract the selling price of 20 articles from the selling price of all articles to find the selling price of 80 articles. Now find the cost price of 80 articles. Then find the gain on 80 articles. After that find the gain percent by dividing gain by cost price of 80 articles.

Complete step-by-step solution:
The cost price of 100 articles is Rs. 4000.
Then, find the cost price per article,
$ \Rightarrow $ Cost price of 1 article $ = \dfrac{{4000}}{{100}}$
Cancel out the common factor,
$ \Rightarrow $ Cost price of 1 article $ = 40$
As Ravish sold 20 articles at a gain of $20\% $.
$ \Rightarrow $ Cost price of 20 articles $ = 40 \times 20$
Multiply the terms,
$ \Rightarrow $ Cost price of 20 articles =$800$
Now, find the selling price of 20 articles,
$ \Rightarrow $ Selling price of 20 articles $ = 800 + \dfrac{5}{{100}} \times 800$
Cancel out common factor and multiply,
$ \Rightarrow $ Selling price of 20 articles $ = 800 + 40$
Add the terms,
$ \Rightarrow $ Selling price of 20 articles $ = 840$
Now to get a 20% gain on the whole transaction,
$ \Rightarrow $ Selling price of all articles $ = 4000 + \dfrac{{20}}{{100}} \times 4000$
Cancel out common factor and multiply,
$ \Rightarrow $ Selling price of all articles $ = 4000 + 800$
Add the terms,
$ \Rightarrow $ Selling price of all articles $ = 4800$
Now, find the selling price of 80 articles by subtracting the selling price of 20 articles from the selling price of all articles,
$ \Rightarrow $ Selling price of 80 articles $ = 4800 - 840$
Subtract the terms,
$ \Rightarrow $ Selling price of 80 articles $ = 3960$
Now, find the cost price of 80 articles,
$ \Rightarrow $ Cost price of 80 articles $ = 80 \times 40$
Multiply the terms,
$ \Rightarrow $ Cost price of 80 articles $ = 3200$
The gain of 80 articles will be,
$ \Rightarrow $ Gain on 80 articles $ = 3960 - 3200$
Subtract the terms,
$ \Rightarrow $ Gain on 80 articles $ = 760$
The gain percent will be,
$ \Rightarrow $ Gain% \[ = \dfrac{{760}}{{3200}} \times 100\]
Cancel out the factors and multiply the terms,
$\therefore $ Gain% $ = 23.75\% $

Hence Ravish must sell the remaining articles at \[23.75\% \] a gain.

Note: Cost Price: The price at which an article is purchased is called its cost price (C.P.)
Selling Price: The price at which an article is purchased is known as its selling price (S.P.)
Profit or Gain: If SP is greater than CP then the seller is said to have profit or gain.
\[Profit = SP - CP\]
\[Profit\% = \dfrac{{Profit}}{{CP}} \times 100\]