CAT 2017Slot 1QAQuestion & Solution
Question
In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is
Options
6%
8%
10%
12%
Solution
1. Concept Used
- Topic: Profit and Loss — Overall Profit Percentage
- Formula: $$ \text{Profit %} = \frac{\text{Total SP} - \text{Total CP}}{\text{Total CP}} \times 100 $$
2. Calculation
Let the cost price of good mangoes be $2x$ per kg. Then the cost price of medium quality mangoes is $\frac{2x}{2} = x$ per kg.
Total Cost Price (CP):
CP of 80 kg good mangoes $= 80 \times 2x = 160x$
CP of 40 kg medium mangoes $= 40 \times x = 40x$
$$\text{Total CP} = 160x + 40x = 200x$$
Selling Price per kg:
The shopkeeper sells all mangoes at a price that is 10% less than the CP of good mangoes:
$$\text{SP per kg} = 2x \times (1 - 0.10) = 2x \times 0.9 = 1.8x$$
Total Selling Price (SP):
Total quantity sold $= 80 + 40 = 120$ kg
$$\text{Total SP} = 120 \times 1.8x = 216x$$
Profit Calculation:
$$\text{Profit} = \text{Total SP} - \text{Total CP} = 216x - 200x = 16x$$
$$\text{Profit %} = \frac{16x}{200x} \times 100 = \frac{16}{200} \times 100 = 8%$$
3. Solution
Answer = Option 2 ✅
The shopkeeper earns an overall profit of 8%.