A trader mixes two types of rice varieties with a cost of Rs.36 and Rs.42. If he sells the mixture of Rs.44 at 10% profit, in what ratio he mixes two types of rice varieties?
Answers
Given data : A trader mixes two types of rice varieties with a cost of Rs 36 and Rs 42. If he sells the mixture of Rs 44 at 10 % profit.
To find : What ratio trader mixes two types of rice varieties ?
Solution :
According to given data,
Let, amount of rice variety mixed with a cost of Rs 36 be x and amount of rice variety mixed with a cost of Rs 42 be y.
⟹ selling price of rice mixture = Rs 44
⟹ profit % on mixture of rice = 10 %
To find cost price of mixture we use formula of profit percentage.
⟹ profit % = [(SP - CP)/CP] * 100
⟹ 10/100 = [(44 - CP)/CP]
⟹ 0.1 = (44 - CP)/CP
⟹ 0.1 = (44/CP) - (CP/CP)
⟹ 0.1 = (44/CP) - 1
⟹ 0.1 = 44/CP
⟹ 0.1 + 1 = 44/CP
⟹ 1.1 = 44/CP
⟹ CP = 44/1.1
⟹ CP = Rs 40
Now,
⟹ sum of cost of two varieties rice = cost price of rice mixture
⟹ 36x + 42y = 40 * (x + y)
⟹ 36x + 42y = 40x + 40y
⟹ 36x - 40x = 40y - 42y
⟹ - 6x = - 2y
⟹ 6x = 2y
⟹ x/y = 2/6
⟹ x/y = 1/3
Answer : Hence, mixing ratio of two type of rice varieties is 1:3.
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