Problem Solving

guerrero wrote:A tea merchant buys 2 varieties of tea - the price of the first being twice of the second. He sells the mixture at 17.50$ per kg, thereby making a profit of 25%. If the ratio of the amounts of the first tea and the second tea in the mixture is 2:3, then find the cost of each tea?

Hi, there. I'm happy to help with this one.

Let me first say -- holy schnikies! This is a challenging question: I would say in the 800+ region.

Let's start with a little backwards calculation. The price of $17.50/kg represents a 25% profit, so it's a 25% increase over the cost.

C*1.25 = 17.25

C = 17.50/1.25 = 14

The mixture costs the tea merchant $14/kg.

He mixes the teas in a 2:3 ratio, and gets one kilogram. 2 + 3 = 5, so he uses 2/5 kg = 0.4 kg of Tea #1 and 3/5 kg = 0.6 kg of Tea #2.

Now, Tea #1 has a price of 2P/kg, and Tea #2 has a price of P/kg.
The 2/5 kg of Tea #1 costs 4P/5.
The 3/5 kg of Tea #2 costs 3P/5
The combined cost is 4P/5 + 3P/5 = 7P/5 for the full kilogram, and this should equal $14.

14 = 7P/5 ---> 70 = 7P, so P = 10 and 2P = 20

The first tea costs $20 and the second tea costs $10.

Check: Suppose he marks up the price to a profit first. The cost of Tea #1 with a 25% profit is $25/kg. The cost of Tea #2 with a 25% profit is $12.50/kg. Now, make a mixture with 2 kg of the first and 3 kg of the second. That would cost 2*(25) + 3*(12.50) = $87.50 for the entire 5 kg mixture. It would have a per-kilogram price of 87.50/5 = $17.50, which is the price the merchant was charging, so our answers work.

Does all that make sense?

Here's another practice question with percent increases:
https://gmat.magoosh.com/questions/30
When you submit your answer to that, the next page will have the complete video explanation.

Let me know if you have any further questions.

Mike