The correct answer is option (B):
1.75
Here's how to solve this problem step-by-step:
First, understand the problem. We have a mixture of two types of rice, and we know their individual costs, the selling price of the mixture, and the profit percentage. We need to find the ratio 'r' in which the two types of rice are mixed.
Let's break down the solution:
1. Calculate the Cost Price (CP) of the mixture: The merchant gains 10% profit by selling at Rs. 13.5C per kg. This means the selling price (SP) is 110% of the cost price. We can use the formula:
SP = CP * (100 + Profit%)/100
13.5C = CP * (100 + 10)/100
13.5C = CP * 110/100
CP = 13.5C * 100/110
CP = 12.27 (approximately)
2. Find the CP per kg of the mixture in terms of 'r': The merchant mixes the rice in the ratio 1:r. The cost of 1 kg of the first variety is Rs. 12.75, and the cost of 'r' kg of the second variety is Rs. 12r.
Total cost = 12.75 + 12r
Total quantity = 1 + r
CP of mixture per kg = (12.75 + 12r) / (1 + r)
3. Equate the two CP values and solve for 'r': We found the CP of the mixture is approximately Rs. 12.27. Now, we can set up the equation:
(12.75 + 12r) / (1 + r) = 12.27
12.75 + 12r = 12.27 + 12.27r
12.75 - 12.27 = 12.27r - 12r
0.48 = 0.27r
r = 0.48 / 0.27
r = 1.777, but the closest answer is 1.75
r = 1.75
Therefore, the value of r is 1.75.