Ratio, Proportion
- The present age of A and B are in the ratio 4 : 5 and after 5 years they will be in the ratio 5 : 6. The present age of A is
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Let the present age of A and B be 4x and 5x years respectively,
According to the question,4x + 5 = 5 5x + 5 6
⇒ 25x + 25 = 24x + 30
⇒ x = 30 – 25 = 5
∴ A’s present age
= 4x = 4 × 5 = 20 yearsCorrect Option: B
Let the present age of A and B be 4x and 5x years respectively,
According to the question,4x + 5 = 5 5x + 5 6
⇒ 25x + 25 = 24x + 30
⇒ x = 30 – 25 = 5
∴ A’s present age
= 4x = 4 × 5 = 20 years
- The ratio of the present age of Rahul and Rashmi is 2 : 1. The ratio of their age after 30 years will be 7 : 6. What is the present age of Rahul ?
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Let the present age of Rahul and Rashmi be 2x and x years respectively.
After 30 years,2x + 30 = 7 x + 30 6
⇒ 12 x +180 = 7x + 210
⇒ 12 x –7x = 210–180⇒ 5 x = 30 ⇒ x = 30 = 6 5
∴ Rahul’s present age
= 2x = 2×6 = 12 yearsCorrect Option: C
Let the present age of Rahul and Rashmi be 2x and x years respectively.
After 30 years,2x + 30 = 7 x + 30 6
⇒ 12 x +180 = 7x + 210
⇒ 12 x –7x = 210–180⇒ 5 x = 30 ⇒ x = 30 = 6 5
∴ Rahul’s present age
= 2x = 2×6 = 12 years
- The ratio of the ages of a father and his son 10 years hence will be 5 : 3, while 10 years ago, it was 3:1. The ratio of the age of the son to that of the father today, is
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Let the age of father 10 years hence is 5x years, then age of son 10 years hence will be 3x years.
According to the question,5x − 10 − 10 = 3 3x − 10 − 10 1 5x − 20 = 3 3x − 20 1
⇒ 5x – 20 = 9x – 60
⇒ 4x = 40 or x = 10
∴ Required ratio
= (3x – 10) : (5x – 10)
= 20 : 40 = 1 : 2Correct Option: A
Let the age of father 10 years hence is 5x years, then age of son 10 years hence will be 3x years.
According to the question,5x − 10 − 10 = 3 3x − 10 − 10 1 5x − 20 = 3 3x − 20 1
⇒ 5x – 20 = 9x – 60
⇒ 4x = 40 or x = 10
∴ Required ratio
= (3x – 10) : (5x – 10)
= 20 : 40 = 1 : 2
- The ratio of the present age of Puneet and Appu is 2 : 3. After 3 years the ratio of their age will be 3 : 4. The present age of Puneet is :
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Let the present age of Puneet and Appu be 2x and 3x years respectively.
After 3 years,2x + 3 = 3 3x + 3 4
⇒ 9x + 9 = 8x + 12
⇒ x = 3
∴ Present age of Puneet
= 2x = 2 × 3 = 6 yearsCorrect Option: B
Let the present age of Puneet and Appu be 2x and 3x years respectively.
After 3 years,2x + 3 = 3 3x + 3 4
⇒ 9x + 9 = 8x + 12
⇒ x = 3
∴ Present age of Puneet
= 2x = 2 × 3 = 6 years
- The ratio of age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be
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The present age of boys are 5x and 6x years respectively.
After 2 years,5x + 2 = 7 6x + 2 8
⇒ 42x + 14 = 40x + 16
⇒ 2x = 2 ⇒ x = 1
Ratio after 12 years
⇒ 5x + 12 : 6x + 12 = 17 : 18Correct Option: C
The present age of boys are 5x and 6x years respectively.
After 2 years,5x + 2 = 7 6x + 2 8
⇒ 42x + 14 = 40x + 16
⇒ 2x = 2 ⇒ x = 1
Ratio after 12 years
⇒ 5x + 12 : 6x + 12 = 17 : 18
