Formulae
1. Age after n years = X + n
2. Age n years ago = X “ n
3. n times the age = nX
4. Age of y = (Ratio of y/Sum of ratios)× sum of ages
5. Age of y = (q/p+q)× A
Exercise : Ages MCQ Questions and Answers
Question 1
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
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Correct Answer : C. 24 years
Description :
Let the present ages of Sameer and Anand be
5x years and 4x years respectively
Then, \( {5x + 3} \over {4x + 3} \) = \( 11 \over 9 \)
⇒ 9(5x+3)=11(4x+3)
⇒ 45x+27=44x+33
⇒ 45x−44x=33−27
⇒ x=6
∴ Anand's present age = 4x = 24 years
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Question 2
At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
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Correct Answer : D. 15 years
Description :
Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
⇒ 4x + 6 = 26
⇒ 4x = 20
⇒ x = 5.
∴ Deepak's age = 3x = 15 years.
Question 3
At present, the ratio between the ages of Raju and Deepak is 7 ∶ 3. After 5 years, Raju's age will be 33 years. What is the present age of Deepak?
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Correct Answer : C. 12 years
Description :
Given:
The ratio between the ages of Raju and Deepak is 7: 3.
After 5 years, Raju's age will be 33 years
Calculations:
Let the present ages of Raju and Deepak be 7x years and 3x years respectively
According to the question
⇒ 7x + 5 = 33
⇒ 7x = 28
⇒ x = 4
Deepak's age = 3x = 12 years
∴ Deepak’s present age is 12 years
Question 4
A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
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Correct Answer : C. 28.8 years
Description :
Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to \( 2 \over 3 \) of P.
=> (48 - P) = \( 2 \over 3 \) P
=> 5P = 144
=> P = 28.8 years
Question 5
A year ago, Akash’s father’s age was 9 times that of Akash. After 3 years his father’s age will be 5 times that of his age. How old will Akash be next year?
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| B. |
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Correct Answer : C. 6 years
Description :
Let one year ago age of Akash’s father be 9x and age of Akash be x.
According to the question
⇒ (9x + 4) / (x + 4) = 5/1
⇒ 9x + 4 = 5x + 20
⇒ x = 4
∴ Age of Akash one year ago = 4 years
Present age of Akash = 4 + 1 = 5 years
∴ Age of Akash next year = 5 + 1 = 6 years
Let the present age of Akash be x.
Let the present age of Akash father be y.
For 1 year ago
⇒ y - 1 = 9(x - 1)
⇒ y = 9x - 8
For after 3 years
⇒ y + 3 = 5(x + 3)
⇒ 9x - 8 + 3 = 5x + 15
⇒ 4x = 20
⇒ x = 5
Age of Akash next year = 5 + 1 = 6 years
∴ The age of Akash next year is 6 years.
Question 6
The average age of a mother and her son is 45 yrs. The ratio of their ages is 3 : 2. Find the age of the son.
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| B. |
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Correct Answer : D. 36 years
Description :
Given:
The average age of Mother and son = 45 yr
Mother and son’s age ratio = 3 : 2
Calculations:
Let the age of Mother be 3x.
Let the age of the son be 2x.
According to the question
⇒ \( {(3x + 2x)} \over 2 \) = 45
⇒ 5x = 90
⇒ x = 18
Son’s age = 2 × 18 = 36 yrs.
∴ Son’s age is 36 years.
As the average of the ages = 45 years
⇒ Sum of their ages = 45 × 2 = 90 years
⇒ Age of the son = \( 2 \over 5 \) × 90 = 36 years
Question 7
The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
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| B. |
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Correct Answer : D. Cannot be determined
Description :
Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, \( {{1 \over 3} * 5x} \over {{1 \over 2} * 6x} \) = \( 5 \over 9 \)
15 = 15
Thus, Shaan's age cannot be determined.
Question 8
Monika’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
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| B. |
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Correct Answer : D. 6
Description :
Given:
Age of Monica's father when she was born = 38 years
Age of Monica's mother when her brother was born = 36 years
Calculation:
Mother’s age when Monika's brother was born = 36
Father’s age when Monika brother was born = 38 + 4 = 42
∴ Required difference in ages = 42 - 36 = 6 years
Mistake Points
1) Reference of age for both the parents are different. The age of the father is given at the time of Monika's birth and the age of the mother is given at the time of Monika's brother's birth.
Hence, we cannot get the difference directly by subtracting the given ages.
2) Age difference will not be 2 years, because the difference between Monika's age and her brother's is 4 and that 4 will be added to the father's age since Monika is older than her brother.
Question 9
Shaan’s current age is four years less than 1.6 times that of Uddalak’s. 26 years ago, Uddalak’s age was one year less than half of Shaan’s age. What is Shaan’s present age in years?
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| D. |
Correct Answer : D. 76 years
Description :
Let the current age of Shaan be x years and of Uddalak be y years
⇒ Given, x = 1.6y – 4 ----(i)
26 years ago,
⇒ y – 26 = 0.5(x – 26) – 1 ----(ii)
Put value of equation (i) in (ii)
⇒ y – 26 = 0.5(1.6y – 30) – 1
⇒ y – 26 = 0.8y – 16
⇒ y = 50 years
⇒ x = 76 years
∴ Shaan’s present age is 76 years.
Question 10
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
| A. |
| B. |
| C. |
| D. |
Correct Answer : B. 24 years
Description :
Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.