John sells 10 litres of a mixture of apple and orange juice, in which

Question

John sells 10 litres of a mixture of apple and orange juice, in which the amount of orange juice in the mixture does not exceed that of apple juice. The cost of apple juice per litre is $8 more than that of orange juice. If John sells the entire mixture for $264 and makes a profit of 10%, then find the highest possible cost of orange juice per litre.

A. 12
B. 20
C. 32
D. 40
E. 50

Are You Up For the Challenge: 700 Level Questions

A. 12
B. 20
C. 32
D. 40
E. 50

Are You Up For the Challenge: 700 Level Questions

yashikaaggarwal · Accepted Answer

Let the cost of orange = x
cost of Apple = x+8

Profit = 10%
The selling price = 264 that is 110% of total cost.
So 100% cost = total cost = 264*100/110 = 240

To find the highest possible cost of orange juice per litre the litres of Orange juice = the litres of Apple juice (since the quantity of orange juice in the mixture does not exceed the quantity of apple juice)

240 = 5*x + 5*(x+8)
240 = 5x+5x+40
200 = 10x
X = 20

Cost of 1 litre of orange juice = 20

Answer is B

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Ilanchezhiyan · Answer

KarishmaB  could you please help with this.how you would solve this question?

KarishmaB · Answer

Overall selling price is $264 and profit is 10%. This means overall cost price is 264*10/11 = $240
This is the cost price for 10 liters so cost price per liter is $24.
Orange juice does not exceed apple juice so at max it can be 50% of the total mixture. So apple and orange juice could hav been mixed in the ratio 1:1 which means their cost prices would be $20 and $28 per liter (so that average of 24 is right in the middle and difference between then is $8)

If orange juice is very very little, then price of apple juice would be almost $24 which means price of orange juice would be almost $16 per liter i.e. lower than $20. So $20 is the maximum possible cost of orange juice.

Answer (B)

Basics here:
https://anaprep.com/arithmetic-weighted-averages/
https://anaprep.com/arithmetic-mixtures/

Bunuel

John sells 10 litres of a mixture of apple and orange juice, in which the amount of orange juice in the mixture does not exceed that of apple juice. The cost of apple juice per litre is $8 more than that of orange juice. If John sells the entire mixture for $264 and makes a profit of 10%, then find the highest possible cost of orange juice per litre.

A. 12
B. 20
C. 32
D. 40
E. 50

Are You Up For the Challenge: 700 Level Questions

John sells 10 litres of a mixture of apple and orange juice, in which

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GMAT Problem Solving (PS) Questions

John sells 10 litres of a mixture of apple and orange juice, in which

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