Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:*Rs. 169.50Rs. 170Rs. 175.50Rs. 180
Question
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:*Rs. 169.50Rs. 170Rs. 175.50Rs. 180
Solution
Let's denote the price of the third variety of tea as X Rs/kg.
According to the problem, the teas are mixed in the ratio 1:1:2. This means that for every 1 kg of the first two types of tea, 2 kg of the third type of tea is used.
The average price of the mixture is given as Rs. 153/kg. We can set up the following equation using the concept of averages:
(1126 + 1135 + 2*X) / (1+1+2) = 153
Solving this equation will give us the price of the third variety of tea.
First, simplify the left side of the equation:
(126 + 135 + 2X) / 4 = 153
Then, multiply both sides of the equation by 4 to get rid of the denominator:
126 + 135 + 2X = 612
Combine like terms:
261 + 2X = 612
Subtract 261 from both sides:
2X = 351
Finally, divide both sides by 2 to solve for X:
X = 351 / 2 = 175.50
So, the price of the third variety of tea is Rs. 175.50 per kg.
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