Question

In what ratio must two kinds of coffee which cost 80 per kg and rs.108 per kg. be mixed such that the resultant mixture costs rs.96 per kg.?

Answer 1

3:4

By alligation method

Answer 2

The value of ratio of two kinds of coffee is 3:4.

Step-by-step explanation:

Given:

First kind of coffee cost rs. 80 per kg.

Second  kind of coffee cost rs.108 per kg.

The resultant coffee mixture costs rs.96 per kg.

To Find:

The value of ratio of two kinds of coffee .

Formula Used:

Quantity of Cheaper/ Quantity of  Dearer =( Cost Price of Dearer - Mean Price)/ (Mean Price – Cost Price of Cheaper)   ---------------- formula no.01

The above is as per  rule of of allegation.

Solution:

As given- First kind of coffee cost rs. 80 per kg.

Cost of 1 kg cheaper first kind of coffee =80

As given - Second  kind of coffee cost rs.108 per kg.

Cost of 1 kg dearer  second kind of coffee =108

As given - The resultant coffee mixture costs rs.96 per kg.

Mean Price of  1 kg  resultant coffee mixture = 96

Applying formula no.01.

Quantity of Cheaper/ Quantity of  Dearer = (Cost Price of Dearer - Mean Price)/( Mean Price – Cost Price of Cheaper)

Putting the values of cost of 1 kg cheaper first kind of coffee, cost of 1 kg dearer  second kind of coffee and mean Price of  1 kg resultant coffee mixture, we get.

Quantity of Cheaper first kind of coffee / Quantity of  Dearer  second kind of coffee  $=\frac{( 108-96)}{( 96-80)}$  

                                      $=\frac{12}{16}$

                                      $=\frac{3}{4}$

Quantity of Cheaper first kind of coffee : Quantity of   dearer  second kind of coffee =3:4

Thus, The value of ratio of two kinds of coffee is 3:4