Question

A retail petrol seller mixes petrol that costs him Rs. 70 per litre with kerosene and sells the mixture at Rs. 77 per litre. What is his profit percentage?
i) He bought 10 litres of kerosene at 60 per litre.
ii) The total profit earned is Rs. 240.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In mixture problems for data sufficiency, the key is usually determining the ratio of the components. If a statement, or a combination of statements, allows you to find this ratio (and the costs of the components), then you can find the average cost and thus the profit/loss percentage.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
This is a data sufficiency problem based on mixtures and profit/loss. To find the profit percentage, we need to know the cost price (CP) and selling price (SP) of the mixture. The SP is given (Rs. 77/litre). The CP of the mixture depends on the cost of petrol and kerosene and the ratio in which they are mixed. \[ \text{Profit %} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \] \[ \text{CP}_{\text{mixture}} = \frac{(\text{Cost of Petrol}) \times (\text{Qty of Petrol}) + (\text{Cost of Kerosene}) \times (\text{Qty of Kerosene})}{(\text{Qty of Petrol}) + (\text{Qty of Kerosene})} \] Let P be the quantity of petrol and K be the quantity of kerosene. \[ \text{CP}_{\text{mixture}} = \frac{70P + (\text{Cost}_K)K}{P+K} \] To find the profit percentage, we essentially need the ratio P:K and the cost of kerosene.
Step 2: Analyze Statement (1)
"He bought 10 litres of kerosene at 60 per litre."
This tells us that K = 10 litres and the cost of kerosene is Rs. 60/litre. We can now write the CP of the mixture as: \[ \text{CP}_{\text{mixture}} = \frac{70P + 60(10)}{P+10} = \frac{70P + 600}{P+10} \] However, we do not know the quantity of petrol, P. The CP of the mixture, and thus the profit percentage, will change depending on the value of P. Since we cannot find a unique profit percentage, Statement (1) is NOT sufficient.
Step 3: Analyze Statement (2)
"The total profit earned is Rs. 240."
Total Profit = Total Revenue - Total Cost. Total Revenue = \(77 \times (P+K)\). Total Cost = \(70 \times P + (\text{Cost}_K) \times K\). \[ 240 = 77(P+K) - (70P + (\text{Cost}_K)K) \] This equation has three unknowns: P, K, and Cost\(_K\). We cannot solve for the ratio P:K. Thus, Statement (2) is NOT sufficient.
Step 4: Combine Statements (1) and (2)
From (1), we know K = 10 and Cost\(_K\) = 60. From (2), we have the total profit equation. We can substitute the values from (1) into the equation from (2): \[ 240 = 77(P+10) - (70P + 60 \times 10) \] \[ 240 = 77P + 770 - 70P - 600 \] \[ 240 = 7P + 170 \] \[ 7P = 70 \implies P = 10 \] Now we know the quantity of petrol is 10 litres. Since we know both P=10 and K=10, we can find the CP of the mixture. \[ \text{CP}_{\text{mixture}} = \frac{70(10) + 60(10)}{10+10} = \frac{700 + 600}{20} = \frac{1300}{20} = 65 \] The CP is Rs. 65/litre. The SP is Rs. 77/litre. We can now calculate a unique profit percentage: \[ \text{Profit %} = \frac{77 - 65}{65} \times 100 = \frac{12}{65} \times 100 \] Since a unique answer can be found, the statements together are sufficient.
Step 5: Final Answer
Neither statement alone is sufficient, but both statements together are sufficient.