Ratio, Proportion
- The sum of three numbers is 540. The ratio of second to third is 9 : 13 and that of first to third is 2 : 7. The third number is :
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Let three numbers be a, b and c respectively.
According to the question,
a + b + c = 540
and b : c = 9 : 13
a : c = 2 : 7∴ a × c = 2 × 13 c b 7 9 ⇒ a = 26 b 63
∴ b : c = 9 : 13 = 63 : 91
∴ a : b : c = 26 : 63 : 91
Sum of the terms of ratio
= 26 + 63 + 91 = 180∴ c = 91 × 540 = 273 180 Correct Option: A
Let three numbers be a, b and c respectively.
According to the question,
a + b + c = 540
and b : c = 9 : 13
a : c = 2 : 7∴ a × c = 2 × 13 c b 7 9 ⇒ a = 26 b 63
∴ b : c = 9 : 13 = 63 : 91
∴ a : b : c = 26 : 63 : 91
Sum of the terms of ratio
= 26 + 63 + 91 = 180∴ c = 91 × 540 = 273 180
- Two numbers are in the ratio 3 : 5. If 6 is added to each of them, the ratio becomes 2 : 3. The numbers are
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Let the numbers be 3x and 5x.
According to the question,3x + 6 = 2 5x + 6 3
⇒ 10x + 12 = 9x + 18
⇒ 10x – 9x = 18 – 12
⇒ x = 6
Numbers are :
3x = 3 × 6 = 18 and
5x = 5 × 6 = 30Correct Option: D
Let the numbers be 3x and 5x.
According to the question,3x + 6 = 2 5x + 6 3
⇒ 10x + 12 = 9x + 18
⇒ 10x – 9x = 18 – 12
⇒ x = 6
Numbers are :
3x = 3 × 6 = 18 and
5x = 5 × 6 = 30
- Two numbers whose sum is 84 can not be in the ratio
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According to the question,
The number 84 must be a multiple of sum of the terms of ratio.
For ratio 3 : 2,
Sum of the terms of ratio
= 3 + 2 = 5 which is not a factor of 84.Correct Option: D
According to the question,
The number 84 must be a multiple of sum of the terms of ratio.
For ratio 3 : 2,
Sum of the terms of ratio
= 3 + 2 = 5 which is not a factor of 84.
- Three numbers are in the ratio 5:7:12. If the sum of the first and the third numbers is greater than the second number by 50. The sum of the three numbers is
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Let the numbers be 5x, 7x and 12x.
According to the question,
5x + 12x = 7x + 50
⇒ 17x – 7x = 50
⇒ 10x = 50⇒ x = 50 = 5 10
∴ Required sum
= 5x + 7x + 12x = 24x
= 24 × 5 = 120Correct Option: B
Let the numbers be 5x, 7x and 12x.
According to the question,
5x + 12x = 7x + 50
⇒ 17x – 7x = 50
⇒ 10x = 50⇒ x = 50 = 5 10
∴ Required sum
= 5x + 7x + 12x = 24x
= 24 × 5 = 120
- Two numbers are in ratio 5 : 8. If their difference is 48, then the smaller number is
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Numbers = 5x and 8x
According to the question,
8x – 5x = 48
⇒ 3x = 48 ⇒ x = 16
∴ Smaller number = 5x
= 5 × 16 = 80Correct Option: A
Numbers = 5x and 8x
According to the question,
8x – 5x = 48
⇒ 3x = 48 ⇒ x = 16
∴ Smaller number = 5x
= 5 × 16 = 80
