Ratio, Proportion
- What must be added to each term of the ratio 7 : 13, so that the ratio becomes 2 : 3 .
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Let x be added to each term .
Then , 7 + x = 2 13 + x 3
⇒ 3 (7 + x) = 2 (13 + x)
⇒ 21 + 3x = 26 + 2x
⇒ 3x – 2 x 26 – 21
⇒ x = 5
∴ 5 must be added to each term .Correct Option: B
Let x be added to each term .
Then , 7 + x = 2 13 + x 3
⇒ 3 (7 + x) = 2 (13 + x)
⇒ 21 + 3x = 26 + 2x
⇒ 3x – 2 x 26 – 21
⇒ x = 5
∴ 5 must be added to each term .
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If x = 2 find the ratio of 9x + 6y : 5x + 3y . y 5
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We have, x = 2 y 5 ∴ 9x + 6y : 5x + 3y = 9x + 6y 5x + 3y = 9 x + 6 y 5 x + 3 y
(On dividing Numerator and Denominator by y)= 9 × 2 + 6 5 5 × 2 + 3 5 = 18 + 30 5 2 + 3 = 48 = 48 5 × 5 25 Correct Option: A
We have, x = 2 y 5 ∴ 9x + 6y : 5x + 3y = 9x + 6y 5x + 3y = 9 x + 6 y 5 x + 3 y
(On dividing Numerator and Denominator by y)= 9 × 2 + 6 5 5 × 2 + 3 5 = 18 + 30 5 2 + 3 = 48 = 48 5 × 5 25
- If (2x + 3) : (5x – 38) be the duplicate ratio of √5 : √ 6 . Find the value of x .
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Since (2x + 3) : (5x – 38 ) is the duplicate ratio of √5 : √6,
therefore2x + 3 = 
√5 
2 5x − 38 √6 ⇒ 2x + 3 = 5 5x − 38 6
⇒ 6 (2x + 3)= 5 (5x – 38 )
⇒ 12x + 18 = 25x – 190
⇒ 25x – 12x = 18 + 190
⇒ 13x = 208⇒ x = 208 = 16 13 Correct Option: C
Since (2x + 3) : (5x – 38 ) is the duplicate ratio of √5 : √6,
therefore2x + 3 = √5 2 5x − 38 √6 ⇒ 2x + 3 = 5 5x − 38 6
⇒ 6 (2x + 3)= 5 (5x – 38 )
⇒ 12x + 18 = 25x – 190
⇒ 25x – 12x = 18 + 190
⇒ 13x = 208⇒ x = 208 = 16 13
- If A : B = 1 : 2 , B : C = 3 : 4 , C : D = 2 : 3 and D : E = 3 : 4 , then find A : B : C : D : E .
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A : B = 1 : 2
B : C = 3 : 4
C : D = 2 : 3
D : E = 3 : 4
∴ A : B : C : D : E
= 1 × 3 × 2 × 3 : 2 × 3 × 2 × 3 : 2 × 4 × 2 × 3 : 2 × 4 × 3 × 3 : 2 × 4 × 3 × 4
= 3 : 6 : 8 :12 : 1 6Correct Option: B
A : B = 1 : 2
B : C = 3 : 4
C : D = 2 : 3
D : E = 3 : 4
∴ A : B : C : D : E
= 1 × 3 × 2 × 3 : 2 × 3 × 2 × 3 : 2 × 4 × 2 × 3 : 2 × 4 × 3 × 3 : 2 × 4 × 3 × 4
= 3 : 6 : 8 :12 : 1 6
- If A : B = 3 : 4 , B : C = 8 : 10 and C : D = 15 : 17, th e n fin d A : B : C : D .
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A : B = 3 : 4 B : C = 8 : 1 0
C : D = 15 : 17
∴ A : B : C : D = 3 × 8 × 15 : 4 × 8 × 15 : 4 × 10 × 15 : 4 × 10 × 17
= 9 : 12 :15 : 17Correct Option: A
A : B = 3 : 4 B : C = 8 : 1 0
C : D = 15 : 17
∴ A : B : C : D = 3 × 8 × 15 : 4 × 8 × 15 : 4 × 10 × 15 : 4 × 10 × 17
= 9 : 12 :15 : 17
