# Word Problem 3

Problem 3: The ratio in which the two qualities of rice at Rs 6 and Rs 4 per kg be mixed respectively in order the mixture may cost Rs 4.8 per kg is ;

a) 2:3                          b) 3:2                         c) 1:4                    d) 1:5

Solution,

We have the following information;

Rice1=Rs 6 per kg

Rice2 = Rs 4 per kg

Mixture = Rs 4.8 per kg

Rice1 : Rice2   =?

We proceed as below;

Let total weight of Rice1 = y kg

Total weight of Rice2 = z kg

Now the data can be arranged as below;

 Price per kg Weight (kg) Total cost in Rs Rice1 6 y 6xy=6y Rice2 4 z 4xz=4z Total 4.8 (given it should be so) y+z 6y+4z

So, we have;

weight of mixture = (y+z) kgs

Price of mixture =4.8 per kg (it should be so according to the question)

So, total cost of mixture =Rs  4.8 (y+z)

But in the table above we calculated total cost of mixture = Rs 6y+4z

This means ;

$4.8 (y+z)=6y+4z$

or

$4.8y+4.8z= 6y+4z$

$4.8y-6y=4z-4.8z$

or

$0.80z=1.20z$

or

$\frac{y}{z}=\frac{0.80}{1.20}$

$=\frac{2}{3}$

or

Rice1 : Rice2 = 2:3

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