Question

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

Answer 1

Let the selling price of $20$ articles be $Rs.x$.

Cost of $100$ articles $=Rs.4000$

Therefore,

Cost price of $1$ articles $=\frac{4000}{100}=Rs.40$

Given that Ravish sold $20$ articles at a gain of $5\%$.

Cost of $20$ articles $=\frac{4000}{100}\times 20=Rs.800$

Let the selling price of $20$ articles be $Rs.x$.

Therefore,

$x=800+5\%$ of 800

$x=800+\frac{5}{100}\times 800$

$\Rightarrow x=800+40=840$

Now to get $20\%$ gain on whole transaction,

Selling price of all the articles should be $120\%$ of cost price.

Let the selling price of all the articles be $Rs.y$

Therefore,

$y=4000+20\%$ of $4000$

$y=4000+\frac{20}{100}\times 4000$

$\Rightarrow y=4000+800=4800$

Now,

Selling price of $80$ articles $=4800-840=Rs.3960$

Cost price of $80$ articles $=40\times 80=Rs.3200$

Gain $=3960-3200=Rs.760$

Therefore,

Gain $\%$ on $80$ articles $=\frac{760}{3200}\times 100=23.75\%$

Hence Ravish must sell the remaining articles at $23.75\%$ gain.