Ratio, Proportion
- If A : B = 7 : 9 and B : C = 3 : 5, then A : B : C is equal to
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A : B = 7 : 9
B : C = 3 : 5
∴ A : B : C
= 7 × 3 : 9 × 3 : 9 × 5
= 7 : 9 : 15
Second Method :
A : B : C = xp : py : qy
= 7 × 3 : 9 × 3 : 5 × 9
= 21 : 27 : 45
= 7 : 9 : 15Correct Option: C
A : B = 7 : 9
B : C = 3 : 5
∴ A : B : C
= 7 × 3 : 9 × 3 : 9 × 5
= 7 : 9 : 15
Second Method :
A : B : C = xp : py : qy
= 7 × 3 : 9 × 3 : 5 × 9
= 21 : 27 : 45
= 7 : 9 : 15
- If x : y = 5 : 2, then
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x = 5 (Given) y 2 Expression = 8x + 9y 8x + 2y = 8x + 9y y 8x + 2y y = 8 x + 9 y 8 x + 2 y = 8 × 5 + 9 2 8 × 5 + 2 2 = 20 + 9 = 29 20 + 2 22
= 29 : 22Correct Option: C
x = 5 (Given) y 2 Expression = 8x + 9y 8x + 2y = 8x + 9y y 8x + 2y y = 8 x + 9 y 8 x + 2 y = 8 × 5 + 9 2 8 × 5 + 2 2 = 20 + 9 = 29 20 + 2 22
= 29 : 22
- The ratio of the length of a school ground to its width is 5 : 2. If the width is 40 m, then the
length is
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Length : breadth = 5 : 2
Breadth = 40 metre∴ 5 × 40 = 100 metre 2 Correct Option: B
Length : breadth = 5 : 2
Breadth = 40 metre∴ 5 × 40 = 100 metre 2
- If x : y : : 2 : 3 and 2 : x : : 4 : 8 the value of y is
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2 = 4 ⇒ 4x = 2 × 8 x 8 ⇒ x = 2 × 8 = 4 4 ∴ x = 2 y 3 ⇒ 4 = 2 y 3
⇒ 2y = 4 × 3⇒ y = 4 × 3 = 6 2 Correct Option: A
2 = 4 ⇒ 4x = 2 × 8 x 8 ⇒ x = 2 × 8 = 4 4 ∴ x = 2 y 3 ⇒ 4 = 2 y 3
⇒ 2y = 4 × 3⇒ y = 4 × 3 = 6 2
- Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 :7. The smaller number is
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Let the numbers be 3x and 5x.
∴ 3x + 10 = 5 5x + 10 7
⇒ 25x + 50 = 21x + 70
⇒ 4x = 20
⇒ x = 5
∴ Smaller number = 3x
= 3 × 5 = 15
Second Method :
Here, a = 3, b = 5, c = 5, d = 7, x = 10
∴ Smaller number= xa(c − d) ∵ a < b ad − bc = 10 × 3(5 − 7) 3 × 7 − 5 × 5 = −60 21 − 25 = 60 = 15 4 Correct Option: C
Let the numbers be 3x and 5x.
∴ 3x + 10 = 5 5x + 10 7
⇒ 25x + 50 = 21x + 70
⇒ 4x = 20
⇒ x = 5
∴ Smaller number = 3x
= 3 × 5 = 15
Second Method :
Here, a = 3, b = 5, c = 5, d = 7, x = 10
∴ Smaller number= xa(c − d) ∵ a < b ad − bc = 10 × 3(5 − 7) 3 × 7 − 5 × 5 = −60 21 − 25 = 60 = 15 4
