Question

Eesha bought two varieties of rice, costing 50 rs per kg and 60 rs pre kg each, and mixed them in some ratio. Then she sold the mixture at 70 rs per kg. Making a profit of 20 percent. What was the ratio of the mixture?



a. 1:5

Answer 1

I think the ratio is 1:5

Answer 2

The ratio of the mixture is 1 : 5

Solution:

Cost price of rice of first variety = 50 rs per kg

Cost price of rice of second variety = 60 rs per kg

Selling price of mixture = 70 rs per kg

Profit = 20 %

Now let us find the cost price of one kg of mixture

Let "a" be the cost price of rice per kg after mixing

Then we get,

$a \times \frac{120}{100} = 70\\\\a = \frac{175}{3}$

Hence the cost price of one kg of mixture = $\frac{175}{3}$

Now by alligation method,

Alligation is the rule which enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a specified price

The image is attached below

$\frac{60 - \frac{175}{3}}{\frac{175}{3} - 50}$

(5/3) / (25/3)

$= \frac{5}{25}$

$= \frac{1}{5}$

The ratio of the mixture is 1 : 5

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