Question

Pure ghee cost Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50 per kg, A shopkeeper sells the mixture at the rate of Rs.96 per kg, thereby making a profit of 20%.In What ratio does he mix the two?

Answer 1

Given:

The cost price of pure ghee = Rs. 100 per kg

The cost price of vegetable oil = Rs. 50 per kg

The shopkeeper sells the mixture at the rate of Rs. 96 per kg, thereby making a profit of 20%

To find:

In what ratio does he mix the two?

Solution:

The S.P. of the mixture = Rs. 96 per kg

Profit = 20%

∴ The C.P. of the mixture is

= $\frac{100}{100 + G\%} \times S.P.$

= $\frac{100}{100 + 20} \times 96$

= $\frac{100}{120} \times 96$

= $Rs.\:80\:per\:kg$

Now, we have the C.P. per kg of pure ghee, vegetable oil and the mixture of both, so by using the mixture and alligation method, we get

Pure Ghee                          Vegetable Oil

  100                                          50

                     Mixture

                         80

   30                                            20

     3                                              2                                        

           

∴ $\bold{\frac{Pure \:Ghee}{Vegetable\;Oil} = \frac{3}{2}}$

Thus, the shopkeeper should mix pure ghee and vegetable oil in the ratio of 3:2.

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