Two types of liquids worth Rs. 40 per litre and Rs 60 per litre are mixed with a third liquid in the ratio of 4:3:3 respectively. If the mixture is sold at Rs. 50 per litre, then find the price of third liquid.(Toppers’ Time: 55 Seconds)a. 50.33b. 51.33c. 52.33d. 53.33e. 54.33
Question
Two types of liquids worth Rs. 40 per litre and Rs 60 per litre are mixed with a third liquid in the ratio of 4:3:3 respectively. If the mixture is sold at Rs. 50 per litre, then find the price of third liquid.(Toppers’ Time: 55 Seconds)a. 50.33b. 51.33c. 52.33d. 53.33e. 54.33
Solution
The problem involves the concept of weighted averages. Here's how to solve it:
Step 1: Understand that the price of the mixture is the weighted average of the prices of the individual liquids. The weights are the ratios in which the liquids are mixed.
Step 2: Set up the equation for the weighted average. The price of the mixture (Rs. 50 per litre) is equal to the sum of the products of the prices and ratios of the individual liquids, divided by the sum of the ratios.
So, 50 = [(404) + (603) + (x*3)] / (4+3+3)
Step 3: Simplify the equation.
50 = [(160) + (180) + (3x)] / 10
Step 4: Solve for x, which represents the price of the third liquid.
500 = 160 + 180 + 3x
500 = 340 + 3x
160 = 3x
x = 160 / 3
x = 53.33
So, the price of the third liquid is Rs. 53.33 per litre. The answer is (d) 53.33.
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