Question

In what ratio should a shopkeeper mix two types of rice, one costing 40 rupees/kg and another costing 20rupees/kg to get a rice variety costing 28 rupees/kg *​

Answer 1

The ratio in which ratio the shopkeeper should mix two types of rice is 2 : 3

Given :

Two types of rice, one costing 40 rupees/kg and another costing 20rupees/kg to get a rice variety costing 28 rupees/kg

To find :

The ratio in which ratio the shopkeeper should mix two types of rice

Solution :

Step 1 of 2 :

Form the equation to find the ratio

Let x kg of first type rice is mixed with y kg of second type rice

The total costing for two tyoes of rice

= Rs. (40x + 20y)

Total amount of two types of rice = (x + y) kg

So price of total of two types of rice (x + y) kg

= Rs. 28(x + y)

By the given condition

$\displaystyle \sf{(40x + 20y) = 28(x + y) }$

Step 2 of 2 :

Find the ratio

$\sf \: (40x + 20y) = 28(x + y)$

$\displaystyle \sf{ \implies 40x + 20y= 28x + 28y }$

$\displaystyle \sf{ \implies 40x - 28x = 28y - 20y }$

$\displaystyle \sf{ \implies 12x = 8y }$

$\displaystyle \sf{ \implies \frac{x}{y} = \frac{8}{12} }$

$\displaystyle \sf{ \implies \frac{x}{y} = \frac{2}{3} }$

$\displaystyle \sf{ \implies x : y = 2 : 3}$

Hence the ratio in which ratio the shopkeeper should mix two types of rice is 2 : 3

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