Question

3. in what ratio must a person mix three kinds of wheat costing him rs. 1.20, rs. 1.44 and rs. 1.74 per kg so that the mixture may be worth rs. 1.41 per kg?

Answer 1

Given:

A person mixes three kinds of wheat costing him rs. 1.20, rs. 1.44 and rs. 1.74 per kg so that the mixture may be worth rs. 1.41 per kg

To find:

The ratio of 3 kinds of wheat in the mixture

Solution:

Firstly, let's assume that the 1st kind of wheat is mixed with 2nd kind of wheat to get a mixture costing Rs. 1.41 per kg

Using the rule of mixture & alligation:

Per kg C.P. of 1st kind              Per kg C.P. of 2nd kind

        1.20                                                 1.44

                     Per kg C.P. of mixture

                               1.41

     

         0.03                                                   0.21

            1                                                          7

∴ $\frac{Quantity\:of\:1st\:kind\:of \:wheat}{Quantity\:of\:2nd\:kind\:of \:wheat} = \frac{1}{7}$

$\implies \bold{\frac{Quantity\:of\:2nd\:kind\:of \:wheat}{Quantity\:of\:1st\:kind\:of \:wheat} = \frac{7}{1}}$ ............. (i)

Secondly, let's assume that the 1st kind of wheat is mixed with 3rd kind of wheat to get a mixture costing Rs. 1.41 per kg

Using the rule of mixture & alligation:

Per kg C.P. of 1st kind              Per kg C.P. of 3rd kind

        1.20                                                 1.74

                     Per kg C.P. of mixture

                               1.41

     

         0.33                                                   0.21

            11                                                        7

∴ $\bold{\frac{Quantity\:of\:1st\:kind\:of \:wheat}{Quantity\:of\:3rd\:kind\:of \:wheat} = \frac{11}{7}}$ ........ (ii)

Now, from (i) & (ii), we get

Qty of 2nd kind    :      Qty of 1st kind     :      Qty of 3rd kind

         7                  :                1

                                             11                :                7

(11 × 7 =) 77            :         (11 × 1 =) 11        :          (1 × 7 =) 7

∴ 1st kind of wheat : 2nd kind of wheat : 3rd kind of wheat = 11 : 77 : 7

Thus, a person must mix three kinds of wheat costing him rs. 1.20, rs. 1.44 and rs. 1.74 per kg in the ratio of 11 : 77 : 7, so that the mixture may be worth rs. 1.41 per kg.

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Answer 2

Answer:

Step-by-step explanation: