Ratio, Proportion
- If x : y = 5 : 6, then (3x2 − 2y2) : (y2 − x2) is
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∴ 3x2 − 2y2 y2 − x2 = 3. x2 − 2 y2 1 − x2 y2 = 3 × 25 − 2 36 1 − 25 36 = 75 − 72 = 3 36 − 25 11
= 3 : 11Correct Option: C
∴ 3x2 − 2y2 y2 − x2 = 3. x2 − 2 y2 1 − x2 y2 = 3 × 25 − 2 36 1 − 25 36 = 75 − 72 = 3 36 − 25 11
= 3 : 11
- If A : B = 2 : 3, B : C = 2 : 4 and C : D = 2 : 5, then A : D is equal to :
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A × B × C = 2 × 2 × 2 B C D 3 4 5 ⇒ A = 2 = 2 : 15 D 15
Second Method :
A : D = xpm : yqn
= 2 × 2 × 2 : 3 × 4 × 5
= 2 : 15Correct Option: A
A × B × C = 2 × 2 × 2 B C D 3 4 5 ⇒ A = 2 = 2 : 15 D 15
Second Method :
A : D = xpm : yqn
= 2 × 2 × 2 : 3 × 4 × 5
= 2 : 15
- If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
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a = b = c = k 3 4 7
⇒ a = 3k, b = 4k and c = 7k⇒ a + b + c = 3k + 4k + 7k c 7k = 14k = 2 = 2 : 1 7k 1 Correct Option: A
a = b = c = k 3 4 7
⇒ a = 3k, b = 4k and c = 7k⇒ a + b + c = 3k + 4k + 7k c 7k = 14k = 2 = 2 : 1 7k 1
- If A : B = 3 : 2 and B : C = 3 : 4 then A : C is equal to
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A : B = 3 : 2
B : C = 3 : 4
∴ A : B : C = 3 × 3 : 2 × 3 : 2 × 4 = 9 : 6 : 8
∴ A : C = 9 : 8
Second Method :
A : C = xp : yq
= 3 × 3 : 2 × 4 = 9 : 8Correct Option: D
A : B = 3 : 2
B : C = 3 : 4
∴ A : B : C = 3 × 3 : 2 × 3 : 2 × 4 = 9 : 6 : 8
∴ A : C = 9 : 8
Second Method :
A : C = xp : yq
= 3 × 3 : 2 × 4 = 9 : 8
- If x : y = 2 : 1, then (x2 − y2) : (x2 + y2) is
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Here, x = 2 ⇒ x2 = 4 y 1 y2 1 ∴ x2 − y2 x2 + y2 = x2 − 1 y2 x2 + 1 y2 = 4 − 1 = 3 = 3 : 5 4 + 1 5 Correct Option: A
Here, x = 2 ⇒ x2 = 4 y 1 y2 1 ∴ x2 − y2 x2 + y2 = x2 − 1 y2 x2 + 1 y2 = 4 − 1 = 3 = 3 : 5 4 + 1 5
