The costs of rice of brand A and rice of brand B are $8 / kg and $4 / kg respectively. If x kg of rice of brand A and y kg of rice of brand B are mixed so that the cost of the mixture is $5 / kg , find x : y .
A. 1 : 2
B. 2 : 1
C. 1 : 3
D. 3 : 1
2 Answers | Add Yours
Let us say we have 1kg of the mixture.
Assume in the mixture we have xkg of brand A. Then from brand B we have ((1-x)kg of rice.
According to the data given;
Cost of brand A in mixture `= x(8) = 8x`
Cost of brand B in mixture` = (1-x)(4) = 4(1-x)`
Total cost of 1kg of mixture `= 8x+4(1-x) = 4(1+x)`
But it is given that the cost of mixture is $5 per kg.
`4(1+x) = 5`
`4x = 1`
`x = 0.25`
`1-x = 0.75`
So the ration of brand A to brand B is 0.25:0.75 = 1:3.
Correct answer is at option C.
The costs of rice of brand A and rice of brand B are $8 / kg and $4 / kg respectively. x kg of rice of brand A is mixed with y kg of rice of brand B. The cost of the mixture is $5 per kg.
The cost of x kg of rice of brand A is 8x and the cost of y kg of rice of brand B is 4y. The mixture of rice obtained is worth 5*(x +y)
8x + 4y = 5*(x +y)
8x + 4y = 5x + 5y
8x - 5x = 5y - 4y
3x = y
x/y = 1/3
The ratio x:y is 1:3
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