Problems on Ages
- The sum of the ages of Yogesh, Prakash and sameer is 93 years. 10 years ago the ratio of their ages was 2 : 3 : 4. What is the present age of sameer ?
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Let the respective ages of Yogesh, Prakash, and Sameer 10 years's ago be 2x, 3x and 4 x years.
∴ Present age of Yogesh = (2x + 10 ) years
∴ Present age of Prakash = (3x + 10 ) years
∴ Present age of sameer = (4x + 10) years
According to question,
(2x + 10) + (3x + 10) + (4x + 10 ) = 93Correct Option: D
Let the respective ages of Yogesh, Prakash, and Sameer 10 years's ago be 2x, 3x and 4 x years.
∴ Present age of Yogesh = (2x + 10 ) years
∴ Present age of Prakash = (3x + 10 ) years
∴ Present age of sameer = (4x + 10) years
According to question,
(2x + 10) + (3x + 10) + (4x + 10 ) = 93
⇒ 9x + 30 = 93
⇒ 9x = 63
∴ x = 7
∴ Present age of Sameer = 4x + 10 = 28 + 10 = 38 years .
- The age of the father 4 years ago was 5 times the age of his son. If the sum of their present ages is 44 years. What is the present age of his son ?
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Let the present age of father and son be x and y years respectively.
From 1st condition,
(x - 4) = 5(y- 4)
⇒ x - 4 = 5y - 20
⇒ x - 5y = -16 .....(i)
From 2nd condition,
⇒ x + y = 44 ...(ii)Correct Option: B
Let the present age of father and son be x and y years respectively.
From 1st condition,
(x - 4) = 5(y- 4)
⇒ x - 4 = 5y - 20
⇒ x - 5y = -16 .....(i)
From 2nd condition,
⇒ x + y = 44 ...(ii)
From equation (i) and (ii)
-6y = -60
⇒ y = 10
∴ Present age of son = 10 years
- The ratio in the ages of A and B, 1 year ago was 3 : 4. While it will be 5 : 6 after 1 year. What is the present age of B ?
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Let the present age of A and B be x and y years respectively
From 1st condition
(x - 1) / (y -1) = 3/4
⇒ 4x - 4 = 3y - 3
⇒ 4x - 3y = 1 ... (i)
From 2nd condition,
(x + 1) / (y + 1) = 5/6
⇒ 6x + 6 = 5y + 5
⇒ 6x - 5y = -1 ...(ii)Correct Option: D
Let the present age of A and B be x and y years respectively
From 1st condition
(x - 1) / (y -1) = 3/4
⇒ 4x - 4 = 3y - 3
⇒ 4x - 3y = 1 ... (i)
From 2nd condition,
(x + 1) / (y + 1) = 5/6
⇒ 6x + 6 = 5y + 5
⇒ 6x - 5y = -1 ...(ii)
Multiplying equation (i) by 3 and equation (ii) by 2 and subtract
y = 5
∴ Present age of B = 5 years
- The ratio in the present ages of Ramesh and Jayesh is 3 : 2. four years ago Ramesh's age was more then Jayesh's age by 6 years. What is the present age of Jayesh ?
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Let the present age of Ramesh be 3x years and the present age of jayesh = 2x years.
According to question, (3x - 4) = (2x - 4) + 6Correct Option: B
Let the present age of Ramesh be 3x years and the present age of jayesh = 2x years.
According to question, (3x - 4) = (2x - 4) + 6
⇒ 3x - 4 = 2x - 4 + 6
⇒ 3x - 4 = 2x + 2
⇒ 3x - 2x = 2 + 4
∴ x = 6
∴ Present age of Jayesh = 2x = 12 years
- A man is five times as old as his son. four years later the sum of their ages will be 56 years. How old is the son at present ?
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Let the present age of man be x years and the age of his son be y years.
From 1st condition,
x = 5y .....(i)
From 2nd condition ,
(x + 4 ) + (y + 4) = 56
⇒ x + y + 8 = 56
⇒ x + y = 48 ... (ii)Correct Option: D
Let the present age of man be x years and the age of his son be y years.
From 1st condition,
x = 5y .....(i)
From 2nd condition ,
(x + 4 ) + (y + 4) = 56
⇒ x + y + 8 = 56
⇒ x + y = 48 ... (ii)
Putting x = 5y in equation (ii)
5y + y = 48
⇒ 6y = 48
⇒ y = 8
∴ Age of son = 8 years
