The ratio of the father’s age to the son’s age is 4 : 1. The product of their ages is 196. What will be the ratio of their ages after 5 years ?
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Solution
Let their age are respectively 4x and x year.
∴ 4x × x = 196
x = 7
∴ Required ratio = (4 × 7 + 5) : 7 + 5
= 33 : 12
= 11 : 4
The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find the sum their present ages.
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Solution
Let the age of the younger person be x years.
Then age of the elder person = (x + 16) years.
∴ 3 (x – 6) = (x + 16 – 6) ⇔ 3x – 18 = x + 10 ⇔ 2x = 28 ⇔ x = 14.
Hence, their present ages are 14 years and 30 years.
So sum of the ages is => 14+30 = 44 years
The ratio between the ages of Kamini and Sonia is 5: 8 respectively and difference between their ages after 5 years will be 12 years. What is the present age of Kamini?
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Solution
8x + 5 – 5x – 5 = 12
x = 4
∴ Requried age = 5 × 4 = 20 years
The ratio between the present age of P and Q is 6: 7. If Q is 4 years old than P, what will be the ratio of the age of P and Q after 5 years?
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Solution
Let P’s age and Q’s age be 6x years and 7x years respectively.
Then, 7x – 6x = 4 ⇔ x = 4.
∴ Required ratio = (6x + 5): (7x + 5) = 29 : 33.
The ratio of present ages of P and Q is 6 : 7. If Q is 4 years older than P, what will be the ratio of ages of P and Q after 4 years?
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Solution
⇒ 7P = 6Q
and Q – P = 4
⇒7Q – 7P = 28
⇒ 7Q – 6Q = 28
⇒ Q = 28 Year & P = 28 – 4 = 24 years
after 4 years P = 28 Q = 32 years P : Q = 7 : 8
Father is aged three times more than his son Ravi. After 8 years, he would be two and a half times of Ravi’s age. After further 8 years, how many times would he be of Ravi’s age ?
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Solution
Let Ravi’s present age be x years. Then, father’s present age = (x + 3x) years = 4x years
(4x + 8) = 5 (x + 8)/2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16) : (x + 16) = 48/24 = 2
Peter is 58 years old. The sum of the ages of Peter and Steven is 69. How old is Steven?
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Solution
Peter = 58
Peter + Steven = 69
58 + Steven = 69
Steven = 69 - 58 = 11 years
Rohit’s age after 15 years will be 5 times his age 5 years back. What is the present age of Rohit?
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Solution
Let Rohit’s present age be x years. Then, Rohit’s age after 15 years = (x + 15) years.
Rohit’s age 5 years back = (x – 5)
∴ x + 15 = 5x – 25 ⇔ 4x = 40 ⇔ x = 10.
Hence, Rohit’s present age = 10 years.
The average age of A, B, C, D and E is 28 years. The average age of D and E is 25 years. What is the average age of A, B and C?
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Solution
average age of A, B and C
=> ((5 × 28) – (2 × 25)) / 3 = (140 – 50) / 3 = 90/3 = 30 years
Gautam is younger than Ravi by 7 years. If their ages are in the respective ratio of 7: 9, how old is Gautam?
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Solution
Let Ravi’s age be x years. Then, Gautam’s age = (x – 7) years.
∴ ⇔ 9x - 63 = 7x ⇔ 2x = 63 ⇔ x = 31.5
Hence, Gautam's age = (x - 7) = 24.5 years