A dealer wants to mix 20 kg of product A costing rupees 2.40 per kg with product B, worth rupees 3.30 per kg to produce a mixture worth rupees 2.70 per kg. How many kilograms of product B should he use?
add up the values of each component:
2.40*20 + 3.30x = 2.70(20+x)
To solve this problem, we need to set up an equation based on the given information.
Let's represent the quantity of product A that will be used as 'x' kg.
The total weight of the mixture will be 20 kg (as mentioned in the question).
The cost of product A is given as rupees 2.40 per kg, so the total cost of product A used will be 2.40 * x rupees.
Similarly, the cost of product B is given as rupees 3.30 per kg, so the total cost of product B used will be 3.30 * (20 - x) rupees.
(20 - x) represents the quantity of product B used, as the total weight of the mixture is 20 kg.
Now, we know that the total cost of the mixture is equal to the cost per kg multiplied by the total weight of the mixture, which is 2.70 * 20 rupees.
Thus, we can set up the equation:
2.40 * x + 3.30 * (20 - x) = 2.70 * 20
Now, we can solve for 'x' to find the quantity of product B that should be used.
2.40x + 3.30(20 - x) = 2.70 * 20
2.40x + 66 - 3.30x = 54
66 - 54 = 3.30x - 2.40x
12 = 0.9x
x = 12 / 0.9
x ≈ 13.33
So, the dealer should use approximately 13.33 kg of product A and (20 - 13.33) ≈ 6.67 kg of product B to produce the desired mixture.