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The average marks of classes P, Q and R in a certain test

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The average marks of classes P, Q and R in a certain test  [#permalink]

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New post 20 Feb 2018, 10:53
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A
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C
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Difficulty:

  45% (medium)

Question Stats:

80% (02:10) correct 20% (01:31) wrong based on 28 sessions

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The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74. The average marks of classes P and R is approximately
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5

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The average marks of classes P, Q and R in a certain test  [#permalink]

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New post 20 Feb 2018, 11:31
souvonik2k wrote:
The average marks of classes P, Q and R in a certain test is 62, 71, and 79 respectively. The average marks of classes P and Q is 66. The average marks of classes Q and R is 74. The average marks of classes P and R is approximately
A) 61.5
B) 64.5
C) 67.5
D) 73.5
E) 75.5


Let the students who sit in class P, Q, and R be x,y, and z

From the question stem, we get the following equations

\(\frac{62x + 71y}{x+y} = 66\) -> \(62x + 71y = 66x + 66y\) -> \(4x = 5y\) -> \(y = \frac{4x}{5}\) -> (1)

\(\frac{71y + 79z}{y+z} = 74\) -> \(71y + 79z = 74y + 74z\) -> \(5z = 3y\) -> \(y = \frac{5z}{3}\) -> (2)

From (1) and (2), we get 12x = 25z (if x=25, z=12)

Therefore, average marks of class P and R are \(\frac{62*25 + 79*12}{37}\) = 67.5 (Option C)
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The average marks of classes P, Q and R in a certain test &nbs [#permalink] 20 Feb 2018, 11:31
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