Rakesh purchased a mobile phone for ₹ 5400 and a refrigerator for ₹ 9600. He sold the mobile phone at three-fourths of its cost price and the refrigerator at $1\frac{1}{3}$ of its cost price. What was the profit/loss? (Bank Recruitment, 2010)

### Concept & Total Profit and Loss To find the overall profit or loss in a transaction involving multiple items, you must calculate the total Cost Price (CP) and the total Selling Price (SP). $$ \text{Total Profit} = \text{Total SP} - \text{Total CP} $$ When an item is sold at a fraction of its cost price, simply multiply the fraction by the cost price to find its selling price. ### Step-by-Step Solution Given: * CP of mobile phone = ₹ 5400 * CP of refrigerator = ₹ 9600 * SP fraction for mobile phone = $3/4$ * SP fraction for refrigerator = $1\frac{1}{3} = 4/3$ Calculation: 1. Calculate the total Cost Price (CP). $$ \text{Total CP} = 5400 + 9600 = 15000 $$ 2. Calculate the Selling Price (SP) of the mobile phone. $$ \text{SP of mobile} = \frac{3}{4} \times 5400 = 3 \times 1350 = 4050 $$ 3. Calculate the Selling Price (SP) of the refrigerator. $$ \text{SP of refrigerator} = \frac{4}{3} \times 9600 = 4 \times 3200 = 12800 $$ 4. Calculate the total Selling Price (SP). $$ \text{Total SP} = 4050 + 12800 = 16850 $$ 5. Find the profit by subtracting Total CP from Total SP. $$ \text{Profit} = 16850 - 15000 = 1850 $$ ### Exam Strategy & Shortcut Instead of calculating the total SP, calculate the individual profit or loss for each item and combine them. Mobile phone: Sold at $3/4$, which is a $1/4$ loss. Loss = $1/4 \times 5400 = 1350$. Refrigerator: Sold at $4/3$, which is a $1/3$ profit. Profit = $1/3 \times 9600 = 3200$. Net outcome = $3200$ (profit) $- 1350$ (loss) = ₹ $1850$ (profit). This method works with smaller numbers and is faster. ### Common Pitfall A common mistake is converting fractions to approximate percentages ($3/4 = 75\%$, $4/3 \approx 133.33\%$) and introducing decimal rounding errors instead of just multiplying the fractions directly against the given values. ### Final Answer Therefore, the correct answer is **(c) ₹ 1850**.