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
The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
| A. |
| B. |
| C. |
| D. |
Correct Answer : D. 70
Description :
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
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50/50
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Question 2
In a family, the age of father, mother, son, and grandson are A, B, C, and D respectively. Given that A - B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years, then (B - C) is:
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 22 years
Description :
Given:
A - B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years
Formula used:
Total age = Average age × total number of peoples
Calculation:
Total age of the family = 4 × 34 = 136 years
A + B + C + D = 136
⇒ A + B = 136 – 33 (∵ C + D = 33)
A + B = 103 years ---- (i)
A – B = 3 years (Given) ----- (ii)
From (i) and (ii)
2A = 106 years
∴ A = 53 years
B = 103 – 53 = 50 years ( from i )
Also C + B = 78 (Given)
⇒ C = 78 – 50 = 28 years
∴ B – C = 50 – 28 = 22 years
Question 3
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 7 : 3
Description :
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Question 4
Three years ago, the ratio of Sonu’s age and Monu’s age was 4 ∶ 5 and three years later, ratio of their ages will be 5 ∶ 6. Find the present age of Monu.
| A. |
| B. |
| C. |
| D. |
Correct Answer : A. 33 years
Description :
Given:
Three years ago, the ratio of Sonu’s age and Monu’s age = 4∶ 5
Three years later, the ratio of their ages = 5 ∶ 6.
Concept Used:
Ratio using.
Calculation:
Let Sonu’s age and Monu’s age three years ago be 4x and 5x .
Then present age of Sonu = 4x + 3
Present age of Monu = 5x + 3
Three years later,
Sonu’s age = 4x + 3 + 3 = 4x + 6
Monu’s age = 5x + 3 + 3 = 5x + 6
According To Question,
\( {(4x + 6)} \over {(5x + 6)} \) = \( 5 \over 6 \)
⇒ 6(4x + 6) = 5(5x + 6)
⇒ 24x + 36 = 25x + 30
⇒ 25x – 24x = 36 – 30
⇒ x = 6 years
So, Present age of Monu = 5x + 3 = 5 × 6 + 3 = 33 years
∴ Present age of Monu is 33 years old.
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?
| A. |
| B. |
| C. |
| D. |
Correct Answer : B. 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 ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
| A. |
| B. |
| C. |
| D. |
Correct Answer : D. None of these
Description :
Let P's age and Q's age be 6x and 7x years respectively.
Then, 7x - 6x = 4 => x = 4
Required ratio = (6x + 4) : (7x + 4)
28 : 32 = 7:8
Question 7
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 ?
| A. |
| B. |
| C. |
| D. |
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 8
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 : D. 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
Question 9
Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
| A. |
| B. |
| C. |
| D. |
Correct Answer : D. 24.5 years
Description :
Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.
⇒ \( {(x - 7)} \over x \) = \( 7 \over 9 \)
⇒ 2x = 63 => x = 31.5
Hence, Sachin's age = (x - 7) = 24.5 years.
Question 10
The ratio between the present ages of P and Q is 5:7 respectively. If the difference between Q's present age and P's age after 6 years is 2. What is the total of P's and Q's present ages?
| A. |
| B. |
| C. |
| D. |
Correct Answer : B. 48 years
Description :
Let the present ages of P and Q be 5x and 7x years respectively.
Then, 7x - (5x + 6) = 2
2x = 8 => x = 4
Required sum = 5x + 7x = 12x = 48 years.