Bunuel wrote:
In what ratio did a grocer mix three varieties of tea that cost $6 per kg, $7 per kg and $8 per kg respectively, to make a profit of 10% by selling the mixture at $7.70 per kg?
(1) The grocer mixed 135 kg of the variety of tea that costs $7 per kg.
(2) The weight of the mixture was 315 kg.
A very interesting question that can be solved using observation and logic.
Given- The grocer has three varieties of tea that cost $6 per kg, $7 per kg and $8 per kg respectively.
- The grocer wants to sell, the mixture so that by selling at 7.70 per kg, he makes a profit of 10%
At this point, let's find what the cost price of the mixture would be -
1.10 * C.P = 7.70
C.P = $7
Thus, the cost price of the mixture should be $7.
Before moving further, let's make a few more inferences -
We know that the three varieties of tea that cost $6 per kg, $7 per kg and $8 per kg respectively. As the cost price needs to stay at $7, we can infer that equal quantities of tea that cost $6 and that cost $8 need to be added to the mixture. This is required so as to offset the price difference and keep the average at $7.
This can be best visualized when the three values are put on a scale as shown. If we want the scale to balance at the center, we have to put equal weight on the edges. However, if we add any weight at the center the balance won't shift on either sides.
$6---------------- $7-----------------$8
Having done some pre-analysis, let's delve into the statements.
Statement 1The grocer mixed 135 kg of the variety of tea that costs $7 per kg.The quantity of the variety of tea that costs $7 per kg is just one of the parameters of the ratio. As the only criteria for the mixture is that the quantity of the variety of tea that costs $6 per kg and the quantity of the variety of tea that costs $8 per kg need to be equal, without any further information, we can take any quantity and form the mixture.
Hence, an unique ratio cannot be determined and the statement is not sufficient
Statement 2The weight of the mixture was 315 kg.Statement 2 gives us the total weight of the mixture, however doesn't provide any details on individual quantities. Therefore, we can have multiple possible ways to form the mixture.
Hence, an unique ratio cannot be determined and the statement is not sufficient
CombinedThe statement combined we get two information
- The weight of the mixture was 315 kg.
- The grocer mixed 135 kg of the variety of tea that costs $7 per kg
Inference:
- The combined weight of the other two varieties ($6 & $8) of tea = 315 - 135 = 180
- As the weight of the other two varieties need to be equal, the quantity of each variety of tea is half the total quantity.
Therefore -
Quantity of tea added of the variety that costs $7 per kg : 135 kg
Quantity of tea added of the variety that costs $6 per kg : 90 kg
Quantity of tea added of the variety that costs $8 per kg : 90 kg
As the quantities are known, we can obtain the ratio.
Sufficient
Option C
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09 Dec 2022, 09:00
45%
(02:06)
wrong 
