Ratio, Proportion
- The ratio of the ages of A and B at present is 3:1. Four years earlier the ratio was 4:1. The
present age of A is
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A’s present age = 3x years
B’s present age = x years
4 years ago,3x − 4 = 4 x − 4 1
⇒ 4x – 16 = 3x – 4
⇒ 4x – 3x = 16 – 4
⇒ x = 12
∴ A’s present age
= 3x = 3 × 12 = 36 yearsCorrect Option: C
A’s present age = 3x years
B’s present age = x years
4 years ago,3x − 4 = 4 x − 4 1
⇒ 4x – 16 = 3x – 4
⇒ 4x – 3x = 16 – 4
⇒ x = 12
∴ A’s present age
= 3x = 3 × 12 = 36 years
- My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was
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16 years ago,
My age = x years
My grandfather’s age = 9x years
After 8 years from the present,
9x + 16 + 8 = 3(x + 8 + 16)
⇒ 9x + 24 = 3x + 24 + 48
⇒ 9x + 24 = 3x + 72
⇒ 9x – 3x = 72 – 24 ⇒ 6x = 48⇒ x = 48 = 8 6
Required ratio 8 years ago,
= (x + 8) : (9x + 8)
= (8 + 8) : (9 × 8 + 8)
= 16 : 80 = 1 : 5Correct Option: D
16 years ago,
My age = x years
My grandfather’s age = 9x years
After 8 years from the present,
9x + 16 + 8 = 3(x + 8 + 16)
⇒ 9x + 24 = 3x + 24 + 48
⇒ 9x + 24 = 3x + 72
⇒ 9x – 3x = 72 – 24 ⇒ 6x = 48⇒ x = 48 = 8 6
Required ratio 8 years ago,
= (x + 8) : (9x + 8)
= (8 + 8) : (9 × 8 + 8)
= 16 : 80 = 1 : 5
- The ratio of the ages of two persons is 4 : 7 and the age of one of them is greater than that of the other by 30 years. The sum of their ages (in years) is
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Ages of the persons = 4x and 7x years.
∴ 7x – 4x = 30 ⇒ 3x = 30
⇒ x = 10
∴ Sum of their ages = 4x + 7x
= 11x years
= 11 × 10 = 110 yearsCorrect Option: A
Ages of the persons = 4x and 7x years.
∴ 7x – 4x = 30 ⇒ 3x = 30
⇒ x = 10
∴ Sum of their ages = 4x + 7x
= 11x years
= 11 × 10 = 110 years
- The ratio between Sumit’s and Prakash’s age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be
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Sumit’s present age = 2x years
Prakash’s present age = 3x years
∴ 3x – 2x = 6
x = 6
∴ Required ratio
= (2 × 6 + 6) : (3 × 6 + 6)
= 18 : 24 = 3 : 4Correct Option: D
Sumit’s present age = 2x years
Prakash’s present age = 3x years
∴ 3x – 2x = 6
x = 6
∴ Required ratio
= (2 × 6 + 6) : (3 × 6 + 6)
= 18 : 24 = 3 : 4
- The present age of two persons are 36 and 50 years respectively. If after n years the ratio of their age will be 3 : 4, then the value of n is
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36 + n = 3 50 + n 4
⇒ 144 + 4n = 150 + 3n
⇒ 4n – 3n = 150 – 144
⇒ n = 6Correct Option: C
36 + n = 3 50 + n 4
⇒ 144 + 4n = 150 + 3n
⇒ 4n – 3n = 150 – 144
⇒ n = 6
