A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?
(1) Q = 455 mL
(2) R = 650 mL
OA D
Source: Magoosh
A chef mixes P ounces of 60% sugar solution with Q ounces of
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From the given information, we have R = P + QBTGmoderatorDC wrote:A chef mixes P ounces of 60% sugar solution with Q ounces of a 10% sugar solution to produce R ounces of a 25% sugar solution. What is the value of P?
(1) Q = 455 mL
(2) R = 650 mL
OA D
Source: Magoosh
From the first solution, we have
Sugar content = 60% of P = 0.6P; and
Water content = 40% of P = 0.4P
From the second solution, we have
Sugar content = 10% of Q = 0.1Q; and
Water content = 90% of Q = 0.9Q
Total sugar content = 0.6P + 0.1Q;
Total water content = 0.4P + 0.9Q
Since is given that the combined solution of R ounces a solution of a 25% sugar solution, we have sugar content in the final solution = 25% of R = 0.25R = 0.25(P + Q)
=> 0.6P + 0.1Q = 0.25(P + Q)
=> P = 3Q/7 ---(1)
We have to get the value of P.
Let's take each statement one by one.
(1) Q = 455 ml
Sufficient. P = 3Q/7 = 3*(455/7) = 195 ml
(2) R = 650 ml
=> R = P + Q = 650
=> Q = 650 - P ---(2)
From (1) and (2), we have
P = 3Q/7 = 3(650 - P)/7
=> 7P = 650*3 - 3P
10P = 650*3
P = 195 ml
The correct answer: D
Hope this helps!
-Jay
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