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All questions of Ages for CLAT Exam

The ratio of the age of a man and his wife is 4 : 3 . At the time of marriage the ratio was 5 : 3 and After 4 years this ratio will become 9 : 7 . How many years ago were they married?
  • a)
    8 years
  • b)
    10 years
  • c)
    11 years
  • d)
    12 years
  • e)
    13 years
Correct answer is option 'D'. Can you explain this answer?

Meera Rana answered
Let the present age of the man and his wife be 4 x and 3 x respectively.
After 4 years this ratio will become 9 : 7 ⇒ ( 4 x + 4 ) : ( 3 x + 4 ) = 9 : 7
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8
Present age of the man = 4 x = 4 × 8 = 32
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24

Six years ago, the ratio of the ages of Vimal and Saroj was 6 : 5 . Four years hence, the ratio of their ages will be 11 : 10 . What is Saroj's age at present?
  • a)
    18
  • b)
    17
  • c)
    16
  • d)
    15
  • e)
    19
Correct answer is option 'C'. Can you explain this answer?

Given that, six years ago, the ratio of the ages of Vimal and Saroj = 6 : 5
Hence we can assume that age of Vimal six years ago = 6x
age of Saroj six years ago = 5x
After 4 years, the ratio of their ages = 11 : 10

Saroj's present age
= ( 5x + 6 ) = 5 x 2 + 6 = 16

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?
  • a)
    6 years
  • b)
    5 years
  • c)
    4 years
  • d)
    3 years
  • e)
    2 years
Correct answer is option 'C'. Can you explain this answer?

Lavanya Menon answered
Let the age of the youngest child = x
Then, the ages of 5 children can be written as x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 )
x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50
⇒ 5 x + 30 = 50
⇒ 5 x = 20

If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18 , then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay's present age?
  • a)
    50 years
  • b)
    60 years
  • c)
    55 years
  • d)
    62 years
  • e)
    58 years
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given:
- Ajay's present age is x
- When 6 years are subtracted from x and the remainder is divided by 18, Rahul's age is obtained.
- Rahul is 2 years younger than Denis, whose age is 5 years.

To find:
Ajay's present age

Solution:
1. When 6 years are subtracted from Ajay's present age, we get (x-6).
2. When (x-6) is divided by 18, we get Rahul's present age.
- (x-6)/18 = Rahul's present age
3. Denis is 2 years older than Rahul.
- Denis's age = Rahul's age + 2
- Denis's age = (x-6)/18 + 2
4. Denis's age is given as 5 years.
- (x-6)/18 + 2 = 5
- (x-6)/18 = 3
- x-6 = 54 (Taking LCM of 18 and 3 as 18)
- x = 60

Therefore, Ajay's present age is 60 years. (Option B)

Present ages of Kiran and Syam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Syam's present age in years?
  • a)
    28
  • b)
    27
  • c)
    26
  • d)
    24
  • e)
    25
Correct answer is option 'D'. Can you explain this answer?

Sravya Joshi answered
Explanation:
Ratio of the present age of Kiran and Syam = 5 : 4
Let present age of Kiran = 5x
Present age of Syam = 4x
After 3 years, ratio of their ages = 11/9
⇒ ( 5 x + 3 ) / ( 4 x + 3 ) = 11/ 9
⇒ 9 ( 5 x + 3 ) = 11 ( 4 x + 3 )
⇒ 45 x + 27 = 44 x + 33
⇒ x = 33 − 27 = 6
Syam's present age = 4 x = 4  x 6 = 24
You can learn tricks to solve Problems on ages through the document: 

The product of the ages of Syam and Sunil is 240 . If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?
  • a)
    16
  • b)
    14
  • c)
    12
  • d)
    10
  • e)
    8
Correct answer is option 'C'. Can you explain this answer?

Pallavi Sharma answered
Let age of Sunil = x
and age of Syam = y
xy = 240 ⋯ ( 1 )

Substituting equation ( 2 ) in equation ( 1 ) . We get

We got a quadratic equation to solve.
Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. But it is more easy to substitute the values given in the choices in the quadratic equation (equation 3 ) and see which choice satisfy the equation.
Here, option A is 10 . If we substitute that value in the quadratic equation, x ( x − 2 ) = 10 × 8 which is not equal to 120
Now try option B which is 12 . If we substitute that value in the quadratic equation, x ( x − 2 ) = 12 × 10 = 120 . See, we got that x = 12
Hence Sunil's age = 12
(Or else, we can solve the quadratic equation by factorization as,

Since x is age and cannot be negative, x = 12
Or by using quadratic formula as


Since age is positive, x = 12

Sandeep's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was 1 : 5 . What is Sandeep's father's age at present?
  • a)
    30 years
  • b)
    40 years
  • c)
    50 years
  • d)
    60 years
  • e)
    65 years
Correct answer is option 'C'. Can you explain this answer?

Sahana Mehta answered
Let the age of Sandeep and his father before 10 years be x and 5 x respectively.
Given that Sandeep's age after six years will be three-seventh of his father's age

Sandeep's father's present age
= 5 x + 10 = 5 × 8 + 10 = 50

The present ages of A,B and C are in proportions 4 : 7 : 9 . Eight years ago, the sum of their ages was 56 . What are their present ages (in years)?
  • a)
    16 , 30 , 38
  • b)
    16 , 30 , 40
  • c)
    16 , 28 , 40
  • d)
    16 , 28 , 36
  • e)
    Insufficient data
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Given:
The present ages of A, B, and C are in proportions 4:7:9.
Eight years ago, the sum of their ages was 56.

To find:
The present ages of A, B, and C.

Solution:
Let the present ages of A, B, and C be 4x, 7x, and 9x respectively.

Eight years ago:
The age of A was (4x - 8)
The age of B was (7x - 8)
The age of C was (9x - 8)

The sum of their ages was 56, so:
(4x - 8) + (7x - 8) + (9x - 8) = 56
20x - 24 = 56
20x = 80
x = 4

Present ages:
The present age of A = 4x = 4 * 4 = 16 years
The present age of B = 7x = 7 * 4 = 28 years
The present age of C = 9x = 9 * 4 = 36 years

Therefore, the present ages of A, B, and C are 16, 28, and 36 years respectively.

Answer:
The correct answer is option D) 16, 28, 36.

The average age of A, B, C and D is 20 years and their ages are in Arithmetic progression. If the youngest among them is 15 years old, what is the age of the oldest one?
  • a)
    15 years
  • b)
    20 years
  • c)
    21 years
  • d)
    25 years
Correct answer is option 'D'. Can you explain this answer?

G.K Academy answered
Since their ages are in Arithmetic progression, the average age of the youngest and oldest must be 20 years.
15 + The age of the oldest one = 20 × 2
The age of the oldest one = 40 – 15 = 25 years
Hence, Option D is correct.

The ratio of the ages of A, B and C is 2 : 3 : 5 respectively. The age of A is what percentage of the difference between the ages of B and C?
  • a)
    60
  • b)
    75
  • c)
    80
  • d)
    100
Correct answer is option 'D'. Can you explain this answer?

Ishaan Roy answered
Understanding the Age Ratio
The ages of A, B, and C are in the ratio 2 : 3 : 5. This means we can represent their ages as:
- Age of A = 2x
- Age of B = 3x
- Age of C = 5x
Here, 'x' is a common multiplier for their ages.

Calculating the Difference Between Ages of B and C
To find the difference between the ages of B and C:
- Difference between ages of B and C = Age of C - Age of B
- Difference = 5x - 3x = 2x

Calculating Age of A as a Percentage of the Difference
Next, we need to find what percentage the age of A is of the difference calculated above:
- Age of A = 2x
- Difference = 2x
Now, we can calculate the percentage:
\[
\text{Percentage} = \left( \frac{\text{Age of A}}{\text{Difference}} \right) \times 100
\]
Substituting the values:
\[
\text{Percentage} = \left( \frac{2x}{2x} \right) \times 100 = 1 \times 100 = 100\%
\]

Conclusion
The age of A is 100% of the difference between the ages of B and C. Therefore, the correct answer is option 'D'.
This demonstrates how the ratio of their ages directly correlates to the percentage calculation based on the differences in their ages.

Father is aged three times more than his son Sunil. After8years, he would be two and a half times of Sunil's age. After further8years, how many times would he be of Sunil's age
a)4times
b)5times
c)2times
d)3times
e)None of these
Correct answer is option 'C'. Can you explain this answer?

Sharmila Singh answered
Explanation:
Let Sunil's present age = x
Then, father's present age = 3x + x = 4x
After 8 years, father's age = 2 half times Sunil's age.
=> (4x + 8) = 2(1/2)(x + 8)
=> 4x + 8 = (5/2)(x + 8)
=> 8x + 16 = 5x + 40
=> 3x = 40-16 = 24
=> x = 24/3 = 8
After 8 years,
Sunil's age = x + 8 + 8 = 24
Father's age = 4x + 8 + 8 = 48
Father's age/ Sunil's age = 48/24 = 2
You can learn tricks to solve Problems on Ages through the document: 

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. What is the ratio of their present ages?
  • a)
    7 : 3
  • b)
    3 : 7
  • c)
    9 : 4
  • d)
    4 : 9
  • e)
    7: 4
Correct answer is option 'A'. Can you explain this answer?

Sagar Sharma answered
Given:
- Age of the father 10 years ago was thrice the age of his son.
- Age of the father 10 years hence will be twice that of his son.

To find:
The ratio of their present ages.

Solution:

Let's assume the present age of the son as 'x' years.
Therefore, the present age of the father will be '3x' years.

10 years ago:
Son's age = x - 10
Father's age = 3x - 10

According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
3x - 10 = 3(x - 10)
3x - 10 = 3x - 30
3x - 3x = -30 + 10
0 = -20

This equation does not hold true, which means our assumption is incorrect.

Let's assume the present age of the father as 'y' years.
Therefore, the present age of the son will be 'y/3' years.

10 years ago:
Son's age = y/3 - 10
Father's age = y - 10

According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
y - 10 = 3(y/3 - 10)
y - 10 = y - 30
y - y = -30 + 10
0 = -20

This equation does not hold true, which means our assumption is incorrect.

Let's assume the present age of the son as 'a' years.
Therefore, the present age of the father will be '2a' years.

10 years ago:
Son's age = a - 10
Father's age = 2a - 10

According to the given condition, the age of the father 10 years ago was thrice the age of his son.
So, we have the equation:
2a - 10 = 3(a - 10)
2a - 10 = 3a - 30
2a - 3a = -30 + 10
-a = -20
a = 20

Therefore, the present age of the son is 20 years.
And the present age of the father is 2a = 2 * 20 = 40 years.

Ratio of their present ages:
Son's age : Father's age
20 : 40
Simplifying the ratio by dividing both terms by 20, we get:
1 : 2

Therefore, the ratio of their present ages is 1 : 2, which is equivalent to 7 : 14.
Hence, option A is the correct answer.

Kiran is younger than Bineesh by 7 years and their ages are in the respective ratio of 7 : 9. How old is Kiran?
  • a)
    25
  • b)
    24.5
  • c)
    24
  • d)
    23.5
  • e)
    25.5
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given, Kiran is younger than Bineesh by 7 years.

Let Kiran's age be x and Bineesh's age be y.

Then, y = x + 7 (as Kiran is younger by 7 years)

Their ages are in the respective ratio of 7:9.

Therefore, x:y = 7:9

We can express y in terms of x as follows:

x:y = 7:9

x:(x+7) = 7:9

9x = 7x + 63

2x = 63

x = 31.5

Therefore, Kiran's age is 31.5 years.

The answer given in the options is in decimal form, so we need to round off the answer to the nearest half.

31.5 is between 31 and 32, so the nearest half is 31.5 itself.

Hence, the correct answer is option (b) 24.5.

The ratio of the ages of A, B and C is 5 : 3 : 5 respectively. The age of A is what percentage of the combined age of B and C?
  • a)
    37.50
  • b)
    40
  • c)
    48
  • d)
    62.50
Correct answer is option 'D'. Can you explain this answer?

Ishaan Roy answered
Understanding the Age Ratio
The ages of A, B, and C are given in the ratio of 5:3:5. This means:
- A's age = 5x
- B's age = 3x
- C's age = 5x
Here, 'x' is a common multiplier.

Calculating the Combined Age of B and C
To find the combined age of B and C:
- B's age + C's age = 3x + 5x = 8x

Finding the Percentage of A's Age to B and C's Combined Age
Now, we need to find what percentage A's age is of the combined age of B and C:
- A's age = 5x
- Combined age of B and C = 8x
The percentage is calculated using the formula:
\[
\text{Percentage} = \left(\frac{\text{A's age}}{\text{Combined age of B and C}}\right) \times 100
\]
Substituting the values:
\[
\text{Percentage} = \left(\frac{5x}{8x}\right) \times 100
\]
The 'x' cancels out:
\[
\text{Percentage} = \left(\frac{5}{8}\right) \times 100 = 62.5\%
\]

Conclusion
Thus, the age of A is **62.50%** of the combined age of B and C. Therefore, the correct answer is option **D**.

Present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. What is father's present age?
  • a)
    30 years
  • b)
    31 years
  • c)
    32 yeas
  • d)
    33 years
  • e)
    34 years
Correct answer is option 'D'. Can you explain this answer?

Let the present age the son = x
Then, present age of the father = 3 x + 3
Given that, three years hence, father's age will be 10 years more than twice the age of the son
⇒ ( 3 x + 3 + 3 ) = 2 ( x + 3 ) + 10
⇒ x = 10
Father's present age
= 3 x + 3 = 3 × 10 + 3 = 33

Ayisha's age is 1 / 6 th of her father's age. Ayisha's father's age will be twice Shankar's age after 10 years. If Shankar's eight birthdays was celebrated two years before, then what is Ayisha's present age.
  • a)
    10 years
  • b)
    12 years
  • c)
    8 years
  • d)
    5 years
  • e)
    9 years
Correct answer is option 'D'. Can you explain this answer?

Ameya Yadav answered
Let Ayisha's present age = x
Then, her father's age = 6 x
Given that Ayisha's father's age will be twice Shankar's age after 10 years. Therefore, Shankar's age after 10 years

Also given that Shankar's eight birthdays was celebrated two years before. Therefore, Shankar's age after 10 years = 8 + 12 = 20

Therefore, Ayisha's present age =5 years

Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.
  • a)
    40 years
  • b)
    38 years
  • c)
    42 years
  • d)
    36 years
  • e)
    44 years
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Problem: Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.

Solution:

Let's assume the present age of Kamal = K and present age of his son = S.

From the given information in the problem, we can form the following equations:

• Kamal was 4 times as old as his son 8 years ago: K - 8 = 4(S - 8)
• After 8 years, Kamal will be twice as old as his son: K + 8 = 2(S + 8)

Now, we need to solve these two equations to find out the present age of Kamal.

Simplifying the first equation:
K - 8 = 4S - 32
K = 4S - 24

Substituting K = 4S - 24 in the second equation:
4S - 24 + 8 = 2(S + 8)
4S - 16 = 2S + 16
2S = 32
S = 16

Now, we can find out Kamal's present age using K = 4S - 24:
K = 4(16) - 24
K = 40

Therefore, the present age of Kamal is 40 years. Hence, the correct option is (a).

A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
  • a)
    23 years
  • b)
    22 years
  • c)
    21 years
  • d)
    20 years
  • e)
    19 years
Correct answer is option 'B'. Can you explain this answer?

Sagar Sharma answered
Given Information:
The man is 24 years older than his son.
In two years, the man's age will be twice the age of his son.

Let's solve the problem step by step:
1. Let's assume:
Let the son's present age be x years.
Therefore, the man's present age would be x + 24 years.
2. After two years:
The son's age will be x + 2 years.
The man's age will be (x + 24) + 2 = x + 26 years.
3. According to the given condition:
In two years, the man's age will be twice the age of his son.
Therefore, we can write the equation as:
x + 26 = 2(x + 2)
4. Solve the equation:
x + 26 = 2x + 4
26 - 4 = 2x - x
22 = x
5. Conclusion:
Therefore, the present age of the son is 22 years. (Option B)

80% of the current age of Vishal is 50% of the current age of Shivam. If the average age of Shivam and Vishal is 39 years, what is the current age of Vishal?
  • a)
    30 years
  • b)
    32 years
  • c)
    36 years
  • d)
    40 years
Correct answer is option 'A'. Can you explain this answer?

Malavika Rane answered

Given Information:
- 80% of Vishal's current age = 50% of Shivam's current age
- Average age of Shivam and Vishal = 39 years

Let's solve the problem step by step:

Step 1: Express the Given Information Mathematically
Let V be the current age of Vishal and S be the current age of Shivam.

- 0.8V = 0.5S (80% of Vishal's age is equal to 50% of Shivam's age)
- (V + S) / 2 = 39 (Average age of Shivam and Vishal is 39)

Step 2: Solve the Equations
From the first equation, we can express S in terms of V:
0.8V = 0.5S
S = 1.6V

Substitute S = 1.6V into the second equation:
(V + 1.6V) / 2 = 39
2.6V / 2 = 39
1.3V = 39
V = 39 / 1.3
V = 30

Step 3: Determine Vishal's Current Age
Therefore, Vishal's current age is 30 years.

Conclusion:
The current age of Vishal is 30 years. Hence, option A (30 years) is the correct answer.

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