Question

An article was sold at ₹ $a$ at a loss of $4\%$. If the article was sold at ₹ $b$, there would be a profit of $20\%$. Then, find a:b.

• A. 5:4
• B. 4:5
• C. 3:4
• D. 2:3

Answer 1

The correct option is B

4:5

When there is a loss, C.P $=\frac{100}{100-\text{loss}\%}\times \text{S.P}$

Selling Price of the article = ₹ a, loss $=4\%$

C.P of the article = ₹$\frac{100}{100-4}\times a=$ ₹ $\frac{25a}{24}$

when there is a profit, S.P $=\frac{100+\text{profit}\%}{100}\times \text{C.P}$

Selling price of article at $20\%$ profit = ₹ b

b $=\frac{100+20}{100}\times \text{₹}\frac{25a}{24}$

$=\frac{120}{100}\times \text{₹}\frac{25a}{24}=\text{₹}\frac{5a}{4}$

$a:b=a:\frac{5a}{4}=4:5$