Question

Given below are two statements:
Statement I: In order to get a mixture worth 16-5/kg, a grocer needs to mix two varieties of pulses costing 15 and 20 per kg respectively in the ratio 7:3.
Statement II: A merchant has 1000 kg rice, part of which he sells at 8% profit and the rest at 16% profit. He gains 14% on the whole. The quantity of rice sold at 16% profit is 750 kg.
In the light of the above statements, choose the correct answer from the option given below:

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true but Statement II is false
• D. Statement I is false but Statement II is true

Answer 1

The Correct Option is A

To determine the correctness of the given statements, we will analyze each statement individually.

Statement I: Mixture of Pulses 

We need to check if mixing pulses costing ₹15/kg and ₹20/kg in the ratio 7:3 gives a mixture worth ₹16.50/kg.

Let: \(C_1\) = Cost of first variety = ₹15/kg \(C_2\) = Cost of second variety = ₹20/kg The Desired mixture cost = ₹16.50/kg

The mixing ratio is 7:3.

The average cost, \(C_m\), is given by the formula for weighted average: \(C_m = \frac{7 \times 15 + 3 \times 20}{7 + 3}\)

Calculating, \(C_m = \frac{105 + 60}{10} = \frac{165}{10} = 16.5\)

Since the calculated mixture cost equals the desired mixture cost, Statement I is true.

Statement II: Rice Profit Calculation

We need to verify if the entire batch yields a 14% profit when part is sold at 8% and the rest (750 kg) at 16%.

Total rice weight = 1000 kg Rice sold at 16% profit = 750 kg Rice sold at 8% profit = 1000 - 750 = 250 kg

Using the average profit formula: \(P = \frac{(250 \times 8) + (750 \times 16)}{1000}\)

Calculating, \(P = \frac{2000 + 12000}{1000} = \frac{14000}{1000} = 14\)

The calculated overall profit is 14%, which confirms Statement II as true.

Conclusion: Both Statement I and Statement II are true.