Ratio, Proportion
- In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5 : 3. The number of girls to be added in the union, so that the ratio of boys to girls in 6 : 5 is
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In the college union,
Number of boys = 5 × 48 = 30 8 Number of girls = 3 × 48 = 18 8
Let the number of girls added be x.∴ 30 = 6 18 + x 5
⇒ 108 + 6x = 150
⇒ 6x = 150 – 108 = 42⇒ x = 42 = 7 6 Correct Option: B
In the college union,
Number of boys = 5 × 48 = 30 8 Number of girls = 3 × 48 = 18 8
Let the number of girls added be x.∴ 30 = 6 18 + x 5
⇒ 108 + 6x = 150
⇒ 6x = 150 – 108 = 42⇒ x = 42 = 7 6
- In a coloured picture of blue and yellow color, blue and yellow colour is used in the ratio of 4 : 3 respectively. If in upper half, blue : yellow is 2 : 3, then in the lower half blue : yellow is
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In coloured picture,
Blue part = 4 7 Yellow part = 3 7
In upper half,Blue part = 2 = 1 5 × 2 5 Yellow part = 3 = 3 5 × 2 10
In lower half,Blue part = 4 − 1 = 20 − 7 7 5 35 = 13 35 Yellow part = 3 − 3 = 30 − 21 7 10 70 = 9 70 ∴ Required ratio = 13 : 9 35 70
= 26 : 9Correct Option: C
In coloured picture,
Blue part = 4 7 Yellow part = 3 7
In upper half,Blue part = 2 = 1 5 × 2 5 Yellow part = 3 = 3 5 × 2 10
In lower half,Blue part = 4 − 1 = 20 − 7 7 5 35 = 13 35 Yellow part = 3 − 3 = 30 − 21 7 10 70 = 9 70 ∴ Required ratio = 13 : 9 35 70
= 26 : 9
- The ratio of 252.5 : 53 is same as
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252.5 : 53
= (52)2.5 : 53
= 55 : 53
= 52 : 1
= 25 : 1Correct Option: D
252.5 : 53
= (52)2.5 : 53
= 55 : 53
= 52 : 1
= 25 : 1
- There are three numbers A, B, C such that twice A is equal to thrice B and four times B is equal to five times C. Then the ratio between A and C is
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As given,
2A = 3B
⇒ A : B = 3 : 2
and, 4B = 5C
⇒ B : C = 5 : 4
∴ A : B : C
= 3 × 5 : 2 × 5 : 2 × 4
= 15 : 10 : 8
∴ A : C = 15 : 8
Second Method :
Here, 2A = 3B i,eA : B = 3 : 2
4B = 5C i,e B : C = 5 : 4
A : C = xp : yq
= 3 × 5 : 2 × 4
= 15 : 8Correct Option: C
As given,
2A = 3B
⇒ A : B = 3 : 2
and, 4B = 5C
⇒ B : C = 5 : 4
∴ A : B : C
= 3 × 5 : 2 × 5 : 2 × 4
= 15 : 10 : 8
∴ A : C = 15 : 8
Second Method :
Here, 2A = 3B i,eA : B = 3 : 2
4B = 5C i,e B : C = 5 : 4
A : C = xp : yq
= 3 × 5 : 2 × 4
= 15 : 8
- On mixing two classes A and B of students having average marks 25 and 40 respectively, the overall average obtained is 30. Find the ratio of the students in the class A and B.
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Number of students in class A = x
Number of students in class B = y
∴ 25x + 40y = 30(x + y)
⇒ 25x + 40y = 30x + 30y
⇒ 30x – 25x = 40y – 30y
⇒ 5x = 10y⇒ x = 10 = 2 : 1 y 5 Correct Option: A
Number of students in class A = x
Number of students in class B = y
∴ 25x + 40y = 30(x + y)
⇒ 25x + 40y = 30x + 30y
⇒ 30x – 25x = 40y – 30y
⇒ 5x = 10y⇒ x = 10 = 2 : 1 y 5
