Ratio, Proportion
- Two numbers are in the ratio of 3 : 5. If 9 be subtracted from each, then they are in the ratio of 12 : 23. Find the numbers.
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According to the question,
3x − 9 = 12 5x − 9 23
(Numbers = 3x and 5x )
⇒ 69x – 207 = 60x – 108
⇒ 9x = 207 – 108 = 99
⇒ x = 11
∴ Required numbers ⇒ 3 × 11
= 33 and 5 × 11 = 55
Second Method :
Here, a = 3, b = 5, c = 12, d = 23, x = 91st Number = xa(d − c) ad − bc = 9 × 3(23 − 12) 3 × 23 − 5 × 12 = 27 × 11 69 − 60 = 27 × 11 = 33 9 2nd Number = xb(d − c) ad − bc = 9 × 5(23 − 12) 3 × 23 − 5 × 12 = 45 × 11 69 − 60 = 45 × 11 = 55 9
Numbers are 33, 55Correct Option: C
According to the question,
3x − 9 = 12 5x − 9 23
(Numbers = 3x and 5x )
⇒ 69x – 207 = 60x – 108
⇒ 9x = 207 – 108 = 99
⇒ x = 11
∴ Required numbers ⇒ 3 × 11
= 33 and 5 × 11 = 55
Second Method :
Here, a = 3, b = 5, c = 12, d = 23, x = 91st Number = xa(d − c) ad − bc = 9 × 3(23 − 12) 3 × 23 − 5 × 12 = 27 × 11 69 − 60 = 27 × 11 = 33 9 2nd Number = xb(d − c) ad − bc = 9 × 5(23 − 12) 3 × 23 − 5 × 12 = 45 × 11 69 − 60 = 45 × 11 = 55 9
Numbers are 33, 55
- Three numbers are in the ratio 1 : 2 : 3. By adding 5 to each of them, the new numbers are in the ratio 2 : 3 : 4. The numbers are:
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Numbers = x,
2x and 3x∴ x + 5 = 2 2x + 5 3
⇒ 4x + 10
= 3x + 15
⇒ x = 5
⇒ Numbers = 5,
10 and 15Correct Option: D
Numbers = x,
2x and 3x∴ x + 5 = 2 2x + 5 3
⇒ 4x + 10
= 3x + 15
⇒ x = 5
⇒ Numbers = 5,
10 and 15
- Ram got twice as many marks in English as in Science. His total marks in English, Science and Maths are 180. If the ratio of his marks in English and Maths is 2 : 3, what is his marks in Science ?
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Marks in English = 2x
Marks in Maths = 3x
Marks in Science = x
∴ x + 2x + 3x = 180
⇒ 6x = 180
⇒ x = 30Correct Option: A
Marks in English = 2x
Marks in Maths = 3x
Marks in Science = x
∴ x + 2x + 3x = 180
⇒ 6x = 180
⇒ x = 30
- In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7 : 3. In order to make this ratio 2 : 1, how many litres of water should be added ?
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Quantity of milk
= 7 × 80 = 56 litres 10
Quantity of water= 3 × 80 = 24 litres 10
Let x litre water be addedThen, 56 = 2 24 + x 1
⇒ 24 + x = 28
x = 4 litresCorrect Option: D
Quantity of milk
= 7 × 80 = 56 litres 10
Quantity of water= 3 × 80 = 24 litres 10
Let x litre water be addedThen, 56 = 2 24 + x 1
⇒ 24 + x = 28
x = 4 litres
- Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each then they are in the ratio 12 : 23. The smaller number is
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Numbers = 3x and 5x (let)
According to question,3x − 9 = 12 5x − 9 23
⇒ 69x – 207 = 60x – 108
⇒ 69x – 60x = 207 – 108⇒ 9x = 99 ⇒ x = 99 = 11 9
∴ Smaller number = 3x
= 3 × 11 = 33Correct Option: B
Numbers = 3x and 5x (let)
According to question,3x − 9 = 12 5x − 9 23
⇒ 69x – 207 = 60x – 108
⇒ 69x – 60x = 207 – 108⇒ 9x = 99 ⇒ x = 99 = 11 9
∴ Smaller number = 3x
= 3 × 11 = 33
