Question

A grocer buys two kinds of tea, one at 32 cents per pound and the other at 40 cents per pound. He mixes together some of each and proposes to sell the blend at 43 cents per pound, making a profit of 25% on the cost. How many pounds of each kind must he use to make a mixture that weighs 100 pounds?

Answer 1

Answer-

He must use 75 pound of first kind and 25 pound of second kind tea.

Solution-

Price of first kind tea per pound = $0.32

Price of second kind tea per pound = $0.40

By selling it at $0.43 per pound he made a profit of 25%

Let the cost price is x, then

$\Rightarrow x+\dfrac{25}{100}x=0.43\\\\\Rightarrow \dfrac{125}{100}x=0.43\\\\\Rightarrow x=0.43\times \dfrac{100}{125}\\\\\Rightarrow x=34$

The cost price of the mixed kind is $0.34

Then, let the amount of first kind tea in the 100 pound mixture is y pound, so the amount of second kind tea is (100-y) pound

So, the price of mixture will be equal to the sum of price of each kind,

$\Rightarrow 0.32y+0.40(100-y)=0.34\times 100$

$\Rightarrow 0.32y+40-0.40y=34$

$\Rightarrow 0.08y=6$

$\Rightarrow y=\dfrac{6}{0.08}=75$

$\Rightarrow y=75$

$\Rightarrow (100-y)=100-75=25$

Therefore, he must use 75 pound of first kind and 25 pound of second kind tea.