Bunuel wrote:

A person mixed three varieties of tea priced at $120 per pound, $135 per pound and $160 per pound. In what ratio did he mix the three varieties of tea?

(1) The price of the mix was $135 per pound.

(2) Only 3 pounds of the variety priced at $135 per pound was used.

Responding to a pm:

3 varieties - $120 (tea1), $135(tea2), $160(tea3)

Stmnt 1: The price of the mix was $135 per pound.

Note that one of the tea was priced at $135 per pound. So the other two teas would be mixed in a ratio to give an average of 135 too.

w1/w2 = (160 - 135) / (135 - 120) = 5/3

So you need to mix $120 and $160 teas in the ratio 5:3. The tea costing $135 can be added in any quantity, the average will stay the same. We don't know the ratio of the quantity of the three teas so not sufficient.

Stmnt 2: Only 3 pounds of the variety priced at $135 per pound was used.

No ratio of the three. Not sufficient.

Using both together, note that we know that tea1 and tea3 were mixed in the ratio 5:3 but we do not know how much exactly of each was used. Did we use 5 pounds and 3 pounds? Or 10 pounds and 6 pounds? Or 15 pounds and 9 pounds? We don't know. We know that 3 pounds of tea2 was used. Depending on how much of tea1 and tea3 were used, the ratio would be different.

If we used 5 pounds and 3 pounds of tea1 and tea3, ratio tea1:tea2:tea3 would be 5:3:3

If we used 10 pounds and 6 pounds of tea1 and tea3, ratio tea1:tea2:tea3 would be 10:3:6

If we used 15 pounds and 9 pounds of tea1 and tea3, ratio tea1:tea2:tea3 would be 15:3:9 = 5:1:3

and so on...

Not sufficient

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Karishma

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