Multiple choice general knowledge sports

A family uses a mixture of a blend of 2 coffees costing Rs. 30 and Rs. 60 respectively.If the family uses only the expensive variety, it will have to spend Rs.450 more. The annual consumption of coffee of the family is 20Kgs. In what ratio are the two blends being used?

  1. 3:1

  2. 2:1

  3. 3:2

  4. 4:5
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A Correct answer
Explanation

Let x be the kg of expensive coffee (Rs.60) and (20-x) be the cheap coffee (Rs.30). Current cost: 60x + 30(20-x). If only expensive: 60 * 20 = 1200. Difference: 1200 - (30x + 600) = 450. Solving gives 600 - 30x = 450, so 30x = 150, x = 5. Ratio of cheap to expensive is 15:5, which is 3:1.

AI explanation

To solve this problem, let's assume that the family is using the cheaper blend in the ratio of 'x' and the more expensive blend in the ratio of 'y'.

According to the given information, the cost of the cheaper blend is Rs. 30, and the cost of the more expensive blend is Rs. 60.

We know that the annual consumption of coffee for the family is 20Kgs.

Therefore, we can set up the following equation:

30x + 60y = 20 * (30 + 450)

Simplifying the equation:

30x + 60y = 600

Dividing the equation by 30:

x + 2y = 20

Rearranging the equation:

x = 20 - 2y

Now let's substitute the value of 'x' in the equation with the given information that using only the expensive variety will cost Rs. 450 more:

30(20 - 2y) + 60y = 450

Simplifying the equation:

600 - 60y + 60y = 450

60y - 60y = 450 - 600

0 = -150

The equation is inconsistent, which means there is no solution. However, this is not possible in this scenario.

Therefore, there must be an error in the question or the given answer choices.

Please double-check the question or provide any additional information if available.

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