Question

In what ratio should two qualities of coffee powder having the rates of ₹47 per kg and ₹32 per kg be mixed in order to get a mixture that would have a rate of ₹37 per kg?

Answer 1

Answer:

1 : 2

Step-by-step explanation:

let taken quantities be X kg and Y kg

=> cost of first= 47X rupees

=> cost of second= 32Y rupees

therefore ,Rate of mixture

= total cost / total quantity

=(47X+ 32Y) / (X+Y)= 37

=> 47X+32Y= 37X+37Y

=> 10X = 5Y

=> X/Y= 1/2

=> ratio = 1 : 2

Answer 2

Two qualities of coffee powder should be mixed in the ratio 1 : 2

Given :

• Two qualities of coffee powder having the rates of ₹ 47 per kg and ₹ 32 per kg be mixed

• The mixture have a rate of ₹ 37 per kg

To find :

The ratio in which two qualities of coffee powder should be mixed

Solution :

Step 1 of 2 :

Form the equation from given data

Let amount of first and second coffee powder are x kg and y kg respectively

Then total price

= ₹ ( 47x + 32y )

Total amount of coffee powder = ( x + y ) kg

Total price of mixture

= ₹ 37( x + y )

So by the given condition

$\displaystyle \sf{ 47x + 32y = 37(x + y) }$

Step 2 of 2 :

Find the required ratio

$\displaystyle \sf{ 47x + 32y = 37(x + y) }$

$\displaystyle \sf{ \implies 47x + 32y = 37x +37 y }$

$\displaystyle \sf{ \implies 47x - 37x = 37 y - 32y}$

$\displaystyle \sf{ \implies 10x = 5y}$

$\displaystyle \sf{ \implies \frac{x}{y} = \frac{5}{10} }$

$\displaystyle \sf{ \implies \frac{x}{y} = \frac{1}{2} }$

$\displaystyle \sf{ \implies x : y = 1 : 2}$

Hence the required ratio = 1 : 2

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