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 ratio of the ages of A and B 8 years ago was 2 : 3. Four years ago, the ratio of their ages was 5 : 7. What will be the ratio of their ages 8 years from now?
| A. |
| B. |
| C. |
| D. |
Correct Answer : B. 4 : 5
Description :
The ratio of the ages of A and B, 8 years ago = 2x : 3x
According to the question
(2x + 4)/(3x + 4) = 5/7
⇒ 7 (2x + 4) = 5 (3x + 4)
⇒ 14x + 28 = 15x + 20
⇒ 15x – 14x = 28 – 20
⇒ x = 8
8 years ago-age of A = 2 × 8 = 16
8 years after-age of A = 16 + 8 + 8 = 32
8 years ago-age of B = 3 × 8 = 24
8 years after-age of B = 24 + 8 + 8 = 40
Ratio of ages of A to B after 8 years = 32 : 40 = 4 : 5
Short Trick:
F3 S.G 15.4.20 Pallavi D3
Ratio of ages of A to B, 8 years ago = 2 : 3 or 4 : 6.
1 unit = 4 years
3 unit = 12 years
∴ Ratio of ages A to B, 8 years after = 4 : 5
View Answer
50/50
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Question 2
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 16, 28, 36
Description :
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
=> 20x = 80
=> x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Question 3
Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
| A. |
| B. |
| C. |
| D. |
Correct Answer : A. Data Inadequate
Description :
Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.
Question 4
The ratio of ages of P and Q four years ago was 2 : 3 and the ratio will become 5 : 7 after four years, Find P’s present age?
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 36 years
Description :
Given:
P : Q (4 years ago) = 2 : 3
P : Q (4 years after) = 5 : 7
Calculation:
Let P’s age 4 years ago = 2m
Q’s age 4 years ago = 3m
Time difference = 8 years
∴ \( {(2m + 8)} \over {(3m + 8)} \) = \( 5 \over 7 \)
⇒ 14m + 56 = 15m + 40
⇒ 15m — 14m = 56 — 40
⇒ m = 16
P’s age 4 years ago = 2m ⇒ 2 × 16 ⇒ 32 years
∴ P’s present age = 32 + 4 ⇒ 36 years
Question 5
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.
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 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 6
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 and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
Question 7
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
| A. |
| B. |
| C. |
| D. |
Correct Answer : A. 10 years
Description :
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
∴ (2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5.
Hence, B's age = 2x = 10 years.
Question 8
Damini is twice as old as Hari. Hari is 5 years older than Nipa. In 5 years, Damini will be three times as old as Nipa. How old is Hari now?
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 5
Description :
Let us consider Nipa’s age is ‘x’,
The age of Hari = x + 5
∴ Damini = 2(x + 5) = 2x + 10
After 5 years,
The age of Damini = 2x + 15
Nipa = x + 5
Dimani’s age will be three times of Nipa’s age :
(2x + 15) = 3(x + 5)
2x + 15 = 3x + 15
3x – 2x = 0;
x = 0
Hence, Hari’s age = 0 + 5 = 5
Hence, Hari is 5 years old now.
Question 9
The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 30, 40
Description :
Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
Question 10
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
| A. |
| B. |
| C. |
| D. |
Correct Answer : D. 14 years
Description :
Let the son's present age be x years. Then, (38 - x) = x
⇒ 2x = 38.
⇒ x = 19.
∴ Son's age 5 years back (19 - 5) = 14 years.