Question

If a person makes a profit of $10\%$ on ${\frac{1}{4}}^{th}$ of the quantity of items sold and a loss of $20\%$ on the rest of the quantity, then his net percent profit or loss is

• A. $15\%$ profit
• B. $15\%$ loss
• C. $12.5\%$ loss
• D. $12.5\%$ profit

Answer 1

The correct option is C $12.5\%$ loss

Let CP of the quantity = Rs. 100

CP of ${\frac{1}{4}}^{th}$ of the items is Rs.25

Profit on ${\frac{1}{4}}^{th}$ of the quantity of items

$=\frac{10}{100}\times CP=\frac{10}{100}\times 25=2.5$

$\therefore$ SP = CP + profit

=25 + 2.5 Rs. 27.5

CP of ${\frac{3}{4}}^{th}$ of the items is Rs.75

Loss on ${\frac{3}{4}}^{th}$ of the quantity $=20\%$ of 75 = Rs. 15

$\Rightarrow$ Selling price (SP) = 75 - 15 = Rs. 60.

$\Rightarrow$ Total SP = 60 + 27.5 =87.5

The total selling price is less than the cost price

$\Rightarrow$ Loss = 100 – 87.5 = Rs. 12.5

$\therefore \%$ Loss $=(\frac{12.5}{100}\times 100)$

$\%Loss=12.5\%$