Question : Ankita sold three toys. The first toy was sold for INR 1,500 at a profit of 25%, the second toy was sold for INR 2,800 at a loss of 50% and the third toy was sold for INR 3,500 at a profit of 25%. Find her total profit or loss percentage.
Option 1: 15.25% loss
Option 2: 15.25% profit
Option 3: 18.75% profit
Option 4: 18.75% loss
Correct Answer: 18.75% loss
Solution : Given, Ankita sold three toys. The first toy was sold for INR 1,500 at a profit of 25%; the second toy was sold for INR 2,800 at a loss of 50% and the third toy was sold for INR 3,500 at a profit of 25%. CP = Cost Price SP = Selling Price For the first toy: $CP_1 = \frac{100}{100\ +\text{ Profit percentage}}×SP_1$ ⇒ $CP_1 = \frac{100}{100+25}×1500$ ⇒ $CP_1 = \frac{100}{125}×1500$ ⇒ $CP_1 = \frac45×1500$ ⇒ $CP_1 = 1200$ For the second toy: $CP_2 = \frac{100}{100\ −\text{ Loss percentage}}×SP_2$ ⇒ $CP_2 = \frac{100}{100−50}×2800$ ⇒ $CP_2 = \frac{100}{50}×2800$ ⇒ $CP_2 = 2×2800$ ⇒ $CP_2 = 5600$ For the third toy: $CP_3 = \frac{100}{100\ +\text{Profit percentage}}×SP_3$ ⇒ $CP_3 = \frac{100}{100+25}×3500$ ⇒ $CP_3 = \frac45×3500$ ⇒ $CP_3 = 2800$ Total CP = $CP_1+CP_2+CP_3$ ⇒ Total CP = 1200 + 5600 + 2800 ⇒ Total CP = 9600 Total SP = $SP_1+SP_2+SP_3$ ⇒ Total SP = 1500 + 2800 + 3500 ⇒ Total SP=7800 Profit or loss = Total SP − Total CP ⇒ Profit or loss = 7800−9600 ⇒ Profit or loss = −1800 Since the value is negative, there is a loss of INR 1800. Percentage loss = $\frac{\text{Loss}}{\text{Total CP}}×100$ ⇒ Percentage loss = $\frac{1800}{9600}×100$ ⇒ Percentage loss = 18.75% Hence, the correct answer is 18.75% loss.
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