Ratio, Proportion
- If A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10, then what is A : D equal to ?
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Here, A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10
∴ A/D = (A/B) x (B/C) x (C/D)Correct Option: A
Here, A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10
∴ A/D = (A/B) x (B/C) x (C/D)
= (2/3) x (5/7) x (3/10)
= 1/7
∴ A : D = 1 : 7
- Calculate the 3rd proportional to 15 and 30.
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Let the 3rd proportional = k
Then, 15 : 30 : : 30 : k
⇒ 15/30 = 30/kCorrect Option: D
Let the 3rd proportional = k
Then, 15 : 30 : : 30 : k
⇒ 15/30 = 30/k
⇒ 15k = 30 x 30
∴ 15k = 30 x 30
∴ k = (30 x 30) / 15 = 60
- Find the mean proportional between 9 and 64.
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Required mean proportional = √9 x 64
Correct Option: B
Required mean proportional = √9 x 64
= 3 x 8 = 24
- If P2 + 4Q2 = 4PQ, then determine P : Q.
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P2 + 4Q2 = 4PQ
⇒ P2 + 4Q2 - 4PQ = 0
⇒ (P - 2Q)2 = 0Correct Option: C
P2 + 4Q2 = 4PQ
⇒ P2 + 4Q2 - 4PQ = 0
⇒ (P - 2Q)2 = 0
⇒ P - 2Q = 0
⇒ P = 2Q
∴ P/Q = 2/1
∴ P : Q = 2 : 1
- If P : Q = 7 : 5, then what is the value of (5P - 2Q) : (3P + 2Q) ?
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Given, P/Q = 7/5
∴ (5P - 2Q) / (3P + 2Q) = (5 x 7 - 2 x 5) / (3 x 7 + 2 x 5)Correct Option: C
Given, P/Q = 7/5
∴ (5P - 2Q) / (3P + 2Q) = (5 x 7 - 2 x 5) / (3 x 7 + 2 x 5)
= (35 - 10) / (21 + 10)
= 25/31
