Ratio, Proportion
- The present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. Then the present age of A in years is :
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A’s present age = 5x years
B’s present age = 6x years
According to the question,
After 7 years,5x + 7 = 6 6x + 7 7
⇒ 36x + 42 = 35x + 49
⇒ 36x – 35x = 49 – 42
⇒ x = 7
A’s present age = 5x = 35 yearsCorrect Option: A
A’s present age = 5x years
B’s present age = 6x years
According to the question,
After 7 years,5x + 7 = 6 6x + 7 7
⇒ 36x + 42 = 35x + 49
⇒ 36x – 35x = 49 – 42
⇒ x = 7
A’s present age = 5x = 35 years
- If 4 years ago the ratio between the ages of P and Q was 5 : 6 and the sum of their ages at
present is 52 years, what is the ratio of their present ages ?
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4 years ago,
P’s age = 5x years
Q’s age = 6x years
According to the question,
5x + 4 + 6x + 4 = 52
⇒ 11x = 52 – 8 = 44⇒ x = 44 = 4 11
∴ Required ratio
= (5x + 4) : (6x + 4)
= (5 × 4 + 4) : (6 × 4 + 4)
= 24 : 28 = 6 : 7Correct Option: B
4 years ago,
P’s age = 5x years
Q’s age = 6x years
According to the question,
5x + 4 + 6x + 4 = 52
⇒ 11x = 52 – 8 = 44⇒ x = 44 = 4 11
∴ Required ratio
= (5x + 4) : (6x + 4)
= (5 × 4 + 4) : (6 × 4 + 4)
= 24 : 28 = 6 : 7
- The current ages of Sonali and Monali are in the ratio 5 : 3. Five years from now, their ages will be in the ratio 10 : 7. Then, Monali’s current age is :
-
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Sonali’s present age = 5x years
Monali’s present age = 3x years
According to the question,
After 5 years,5x + 5 = 10 3x + 5 7 ⇒ x + 1 = 2 3x + 5 7
⇒ 7x + 7 = 6x + 10
⇒ 7x – 6x = 10 – 7
⇒ x = 3
∴ Monali’s present age = 3x
= 9 yearsCorrect Option: C
Sonali’s present age = 5x years
Monali’s present age = 3x years
According to the question,
After 5 years,5x + 5 = 10 3x + 5 7 ⇒ x + 1 = 2 3x + 5 7
⇒ 7x + 7 = 6x + 10
⇒ 7x – 6x = 10 – 7
⇒ x = 3
∴ Monali’s present age = 3x
= 9 years
- The ratio of ages of two persons is 5 : 9 and the age of one of them is greater than the other by 40 years. The sum of their ages in year is
-
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Age of first person = 5x years
Age of second person = 9x years
According to the question,
9x – 5x = 40 ⇒ 4x = 40
⇒ x = 10
∴ Sum of their ages
= 5x + 9x = 14x
= 14 × 10 = 140 yearsCorrect Option: B
Age of first person = 5x years
Age of second person = 9x years
According to the question,
9x – 5x = 40 ⇒ 4x = 40
⇒ x = 10
∴ Sum of their ages
= 5x + 9x = 14x
= 14 × 10 = 140 years
- Eighteen years ago, the ratio of A’s age to B’s age was 8 : 13. Their present ratios are 5 : 7.
What is the present age of A ?
-
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18 years ago,
A’s age = 8x years
B’s age = 13x years
∴ At present,8x + 18 = 5 13x + 18 7
⇒ 56x + 126 = 65x + 90
⇒ 65x – 56x = 126 – 90⇒ 9x = 36 ⇒ x = 36 = 4 9
∴ A’s present age = 8x + 18
= 8 × 4 + 18 = 50 yearsCorrect Option: C
18 years ago,
A’s age = 8x years
B’s age = 13x years
∴ At present,8x + 18 = 5 13x + 18 7
⇒ 56x + 126 = 65x + 90
⇒ 65x – 56x = 126 – 90⇒ 9x = 36 ⇒ x = 36 = 4 9
∴ A’s present age = 8x + 18
= 8 × 4 + 18 = 50 years
