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GMAT - Problem Solving - Ratio & Proportion

A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight (more)

A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

(A) 15
(B) 12
(C) 9
(D) 6
(E) 4

Assume the weight of apples be 6x

therefore wieght of peaches = 5x

weight of grapes = 2x

total weight = 6x + 5x + 2x = 13 x

39 = 13x

x = 3

weight of apples = 6x = 18

weight of grapes = 2x = 6

difference in weight = 18 - 6 = 12 pounds

B is correct

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water (more)

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?
 

Let the amount of orange juice for both days be x

On day 1

amount of water added = x

total volume of orangeade made = 2x

number of glasses of orangeade (n) ∝ volume of orangaede

assume proportionality constant be k

n = k (2x)

let total revenue be R

cost per glass = R/n = R / 2kx = 0.60

=> R/kx = $1.2

On day 2

amount of water added = 2x

Total volume of orangaede made = x + 2x = 3x

number of glasses made = 3 kx (proportionality constant will be same)

Revenue is same as day one = R

cost per glass = R / 3kx = 1/3 * (R/kx) = 1/3 * 1.2 = $0.4

Water consists of Hydrogen and Oxygen in the mass ratio 2:16. What is the mass of hydrogen in 144 grams of water? (more)

Water consists of Hydrogen and Oxygen in the mass ratio 2:16. What is the mass of hydrogen in 144 grams of water?

The ratio between hydrogen and oxygen is 2:16

i.e.

18 grams of water will contain 2g of Hydrogen and 16 g of Oxygen

1g of water will contain 2/18 g of Hydrogen

144g of water will contain 2/18 * 144g of Hydrogen

16g