Raghu sold an article at a loss of 15% . If he had bought the item at 5% less and had sold it for ₹ 195 more, then he would have gained 10%. Find the cost price (in ₹) of the article.

Correct option is A

​Given:

Raglan sold the article at a loss of 15%.

If the article had been bought at 5% less and sold for ₹195 more, he would have gained 10%. 

Formula Used: ​

Profit % and Loss % = $$\frac{Loss \ or \ Profit}{Cost \ Price}\times 100$$ 

where, Loss = Cost Price - Selling Price 

Profit = Selling Price - Cost Price 

Solution:  

Let the cost price be C 

Then, 

$$\text{Selling price} = C - 15\% \text{ of } C \\ \ \\ = C - \frac{15}{100} \times C = \frac{85}{100} \times C = 0.85C$$ 

$$\text{New cost price} = C - 5\% \text{ of } C = \\ \ \\ C - \frac{5}{100} \times C = \frac{95}{100} \times C = 0.95C$$  

Now, 

New selling price = New cost price + 10%  of New cost price

$$\text{New selling price} = 0.95C + 0.10 \times 0.95C\\ \ \\ = 0.95C \times (1 + 0.10) = 0.95C \times 1.10 = 1.045C$$ 

Hence,

$$0.85C + 195 = 1.045C$$ 

$$195 = 1.045C - 0.85C$$ 

$$195 = 0.195C$$ 

$$C = \frac{195}{0.195} = 1000$$ 

Thus, the Cost Price is ₹1000