Question

Two varieties of coffees costing 300 and 375 are mixed together. the cost of the resultant mixture is Rs. 350. find the ratio in which the cheaper coffee is mixed with the dearer coffee.​

Answer 1

The ratio in which the cheaper coffee is mixed with the dearer coffee is 1:2.

Given,

Cost of two varieties of coffees = Rs. 300 and Rs. 375.

The two are mixed.

Cost of resultant mixture = Rs. 350.

To find,

The ratio in which the cheaper coffee is mixed with the dearer coffee.​

Solution,

When the price of two different items to be mixed, and the resultant price of the final mixture is given then, the ratio of quantities in which two items are mixed, is given by

$\frac{amount \hspace{3} (cheaper)}{amount \hspace{3} (dearer)} =\frac{d-m}{m-c} \hfill ...(1)$

where,

m = price of the resultant mixture, or mean price,

d = cost of the dearer item,

c = cost of cheaper item.

Here, it is given that,

the cost of cheaper coffee = c = Rs. 300,

cost of dearer coffee = d = Rs. 375, and,

cost of the resultant mixture = m = Rs. 350.

Thus, the ratio in which the cheaper is mixed with the dearer one, using equation (1), can be determined as follows.

$\frac{amount \hspace{3} (cheaper)}{amount \hspace{3} (dearer)} =\frac{375-350}{350-300}$

$\implies \frac{amount \hspace{3} (cheaper)}{amount \hspace{3} (dearer)} =\frac{25}{50}$

$\implies \frac{amount \hspace{3} (cheaper)}{amount \hspace{3} (dearer)} =\frac{1}{2}.$

⇒ ratio = 1:2.

Therefore, the ratio in which the cheaper coffee is mixed with the dearer coffee is  1:2.

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