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All questions of Problems on Age for CUET Commerce Exam
A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27 . How old is B?- a)10
- b)9
- c)8
- d)7
- e)6
Correct answer is option 'A'. Can you explain this answer?
A is two years older than B who is twice as old as C. The total of the ages of A, B and C is 27 . How old is B?
a)
10
b)
9
c)
8
d)
7
e)
6
|
Lavanya Menon answered |
Let age of C = x .
Then, Age of B = 2x
Age of A = 2 + 2x
Total age of A,B and C =27
B's age =2x=2×5=10
Age of A = 2 + 2x
Total age of A,B and C =27
B's age =2x=2×5=10
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?
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
|
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
⇒ 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
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?
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
|
Harmanjot Singh answered |
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
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?
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
|
|
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
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
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?- a)16 years
- b)18 years
- c)20 years
- d)Can not be determined
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
a)
16 years
b)
18 years
c)
20 years
d)
Can not be determined
e)
None of these
|
Kavya Saxena answered |
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
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?
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
|
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)
- 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)
Ayesha'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?- a)2 years
- b)4 years
- c)6 years
- d)8 years
Correct answer is option 'C'. Can you explain this answer?
Ayesha'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?
a)
2 years
b)
4 years
c)
6 years
d)
8 years
|
|
Anaya Patel answered |
Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.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)12 years
- b)15 years
- c)19 and half
- d)21 years
Correct answer is option 'B'. Can you explain this answer?
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)
12 years
b)
15 years
c)
19 and half
d)
21 years
|
|
Anaya Patel answered |
Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26 
4x = 20
4x = 20x = 5.
Deepak's age = 3x = 15 years.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?
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
|
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 sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:- a)12 years
- b)14 years
- c)18 years
- d)20 years
Correct answer is option 'D'. Can you explain this answer?
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
a)
12 years
b)
14 years
c)
18 years
d)
20 years
|
|
Aarav Sharma answered |
The Problem:
The sum of the present ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. After 6 years, what will be the son's age?
Given Information:
- The present sum of the father and son's ages is 60 years.
- Six years ago, the father's age was five times the age of the son.
Let's solve the problem step by step:
Step 1: Define Variables
Let's assume the present age of the son is 'x' years.
Therefore, the present age of the father will be (60 - x) years.
Step 2: Translate the Given Information into Equations
According to the problem, six years ago, the father's age was five times the age of the son.
So, six years ago, the father's age would be (60 - x - 6) years, and the son's age would be (x - 6) years.
Step 3: Set up Equations
According to the given information, the father's age six years ago was five times the son's age six years ago.
Therefore, we can set up the equation: (60 - x - 6) = 5(x - 6).
Step 4: Solve the Equation
Let's solve the equation we set up in the previous step:
(60 - x - 6) = 5(x - 6)
54 - x = 5x - 30
4x = 84
x = 21
Step 5: Find the Son's Age After 6 Years
To find the son's age after 6 years, we need to add 6 to the current age of the son.
Son's age after 6 years = 21 + 6 = 27 years.
Conclusion:
After 6 years, the son's age will be 27 years. Therefore, the correct answer is option 'D' (20 years).
The sum of the present ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. After 6 years, what will be the son's age?
Given Information:
- The present sum of the father and son's ages is 60 years.
- Six years ago, the father's age was five times the age of the son.
Let's solve the problem step by step:
Step 1: Define Variables
Let's assume the present age of the son is 'x' years.
Therefore, the present age of the father will be (60 - x) years.
Step 2: Translate the Given Information into Equations
According to the problem, six years ago, the father's age was five times the age of the son.
So, six years ago, the father's age would be (60 - x - 6) years, and the son's age would be (x - 6) years.
Step 3: Set up Equations
According to the given information, the father's age six years ago was five times the son's age six years ago.
Therefore, we can set up the equation: (60 - x - 6) = 5(x - 6).
Step 4: Solve the Equation
Let's solve the equation we set up in the previous step:
(60 - x - 6) = 5(x - 6)
54 - x = 5x - 30
4x = 84
x = 21
Step 5: Find the Son's Age After 6 Years
To find the son's age after 6 years, we need to add 6 to the current age of the son.
Son's age after 6 years = 21 + 6 = 27 years.
Conclusion:
After 6 years, the son's age will be 27 years. Therefore, the correct answer is option 'D' (20 years).
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)1 year
- b)2 years
- c)25 years
- d)Data inadequate
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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)
1 year
b)
2 years
c)
25 years
d)
Data inadequate
e)
None of these
|
|
Aarav Sharma answered |
Given Information:
- Q is as much younger than R as he is older than T.
- The sum of the ages of R and T is 50 years.
To find:
- The definite difference between R and Q's age.
Let's assume Q's age as x years.
According to the given information, the age difference between Q and R is the same as the age difference between Q and T.
Age difference between Q and R: x - T
Age difference between Q and T: R - x
According to the given information, the sum of R and T's ages is 50 years.
Therefore, we can write the equation:
R + T = 50
Solving the Equations:
From the equation R + T = 50, we can express T in terms of R:
T = 50 - R
Substituting the value of T in the equation R - x = x - T, we get:
R - x = x - (50 - R)
R - x = x + R - 50
2R - 50 = 2x
2R = 2x + 50
R = x + 25
The difference between R and Q's age is given by:
Difference = R - Q
Substituting the values of R and Q, we get:
Difference = (x + 25) - x
Difference = 25
Therefore, the definite difference between R and Q's age is 25 years.
- Q is as much younger than R as he is older than T.
- The sum of the ages of R and T is 50 years.
To find:
- The definite difference between R and Q's age.
Let's assume Q's age as x years.
According to the given information, the age difference between Q and R is the same as the age difference between Q and T.
Age difference between Q and R: x - T
Age difference between Q and T: R - x
According to the given information, the sum of R and T's ages is 50 years.
Therefore, we can write the equation:
R + T = 50
Solving the Equations:
From the equation R + T = 50, we can express T in terms of R:
T = 50 - R
Substituting the value of T in the equation R - x = x - T, we get:
R - x = x - (50 - R)
R - x = x + R - 50
2R - 50 = 2x
2R = 2x + 50
R = x + 25
The difference between R and Q's age is given by:
Difference = R - Q
Substituting the values of R and Q, we get:
Difference = (x + 25) - x
Difference = 25
Therefore, the definite difference between R and Q's age is 25 years.
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)5 : 2
- b)7 : 3
- c)9 : 2
- d)13 : 4
Correct answer is option 'B'. Can you explain this answer?
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)
5 : 2
b)
7 : 3
c)
9 : 2
d)
13 : 4
|
Sagar Sharma answered |
Given Information:
- 10 years ago, the father's age was thrice the age of his son.
- 10 years hence, the father's age will be twice that of his son.
Let's Solve the Problem:
Let the present age of the son be S and the present age of the father be F.
- According to the first condition, 10 years ago:
F - 10 = 3(S - 10) (Father's age 10 years ago was thrice his son's age)
F - 10 = 3S - 30
F = 3S - 20
- According to the second condition, 10 years hence:
F + 10 = 2(S + 10) (Father's age 10 years hence will be twice his son's age)
F + 10 = 2S + 20
F = 2S + 10
- Equating the two expressions for F:
3S - 20 = 2S + 10
S = 30
- Substituting S = 30 into F = 2S + 10:
F = 2(30) + 10
F = 70
Therefore, the present ages of the father and son are 70 and 30 respectively.
Ratio of their present ages:
70:30
7:3
Therefore, the ratio of their present ages is 7:3.
At present, the ratio between the ages of Shekhar and Shobha is 4 : 3 . After 6 years, Shekhar's age will be 26 years. Find out the age of Shobha at present?- a)15 years
- b)14 years
- c)13 years
- d)12 years
- e)11 years
Correct answer is option 'A'. Can you explain this answer?
At present, the ratio between the ages of Shekhar and Shobha is 4 : 3 . After 6 years, Shekhar's age will be 26 years. Find out the age of Shobha at present?
a)
15 years
b)
14 years
c)
13 years
d)
12 years
e)
11 years
|
Mihir Nambiar answered |
After 6 years, Shekhar's age will be 26 years
Therefore, Present age of Shekhar = 26 − 6 = 20
Let present age of Shobha = x
Therefore, Present age of Shekhar = 26 − 6 = 20
Let present age of Shobha = x
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?
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
|
|
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
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?
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
|
|
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
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 three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).- a)8, 20, 28
- b)16, 28, 36
- c)20, 35, 45
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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)
8, 20, 28
b)
16, 28, 36
c)
20, 35, 45
d)
None of these
|
Ravi Singh answered |
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.The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?- a)10
- b)20
- c)30
- d)40
- e)50
Correct answer is option 'C'. Can you explain this answer?
The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?
a)
10
b)
20
c)
30
d)
40
e)
50
|
|
Abhishek Choudhury answered |
Let present age of the elder person = x and
present age of the younger person = x − 16
present age of the younger person = x − 16
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age of my father when my brother was born?- a)35 years
- b)34 years
- c)33 years
- d)32 years
- e)31 years
Correct answer is option 'D'. Can you explain this answer?
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age of my father when my brother was born?
a)
35 years
b)
34 years
c)
33 years
d)
32 years
e)
31 years
|
|
Arka Basu answered |
Let my age = x
Then
My brother's age = x + 3
My mother's age = x + 26
My sister's age = ( x + 3 ) + 4 = x + 7 My father's age = ( x + 7 ) + 28 = x + 35
Age of my father when my brother was born = x + 35 − ( x + 3 ) = 32
Then
My brother's age = x + 3
My mother's age = x + 26
My sister's age = ( x + 3 ) + 4 = x + 7 My father's age = ( x + 7 ) + 28 = x + 35
Age of my father when my brother was born = x + 35 − ( x + 3 ) = 32
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?
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
|
|
Chirag Sen answered |
Let present age of A,B and C be 4 x , 7 x and 9 x respectively.
(4x−8)+(7x−8)+(9x−8)=56
⇒20x=80
⇒x=4
Hence present age of A, B and C are
4 × 4 , 7 × 4 and 9 × 4 respectively.
i.e., 16 , 28 and 36 respectively.
(4x−8)+(7x−8)+(9x−8)=56
⇒20x=80
⇒x=4
Hence present age of A, B and C are
4 × 4 , 7 × 4 and 9 × 4 respectively.
i.e., 16 , 28 and 36 respectively.
Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:43:4, what will be the total of their present ages?- a)45
- b)40
- c)35
- d)30
- e)25
Correct answer is option 'C'. Can you explain this answer?
Ten years ago, P was half of Q's age. If the ratio of their present ages is 3:43:4, what will be the total of their present ages?
a)
45
b)
40
c)
35
d)
30
e)
25
|
|
Chirag Roy answered |
Let present age of P and Q be 3x
and 4x respectively.
Ten years ago, P was half of Q's age
Total of their present ages
=3x+4x=7x=7×5=35
and 4x respectively.
Ten years ago, P was half of Q's age
Total of their present ages
=3x+4x=7x=7×5=35
The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?- a)48
- b)45
- c)43
- d)44
- e)46
Correct answer is option 'D'. Can you explain this answer?
The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
a)
48
b)
45
c)
43
d)
44
e)
46
|
|
Aditya Gupta answered |
Total age of all students
= 22 × 21
= 22 × 21
Total age of all students + Age of the teacher = 23 × 22
Sachin's age after 15 years will be 5 times his age 5 years back. Find out the present age of Sachin?- a)10 years
- b)11 years
- c)12 years
- d)13 years
- e)14 years
Correct answer is option 'A'. Can you explain this answer?
Sachin's age after 15 years will be 5 times his age 5 years back. Find out the present age of Sachin?
a)
10 years
b)
11 years
c)
12 years
d)
13 years
e)
14 years
|
|
Gitanjali Kumar answered |
Let present age of Sachin = x . Then,
( x + 15 ) = 5 ( x − 5 )
⇒ 4 x = 40
⇒ x = 10
( x + 15 ) = 5 ( x − 5 )
⇒ 4 x = 40
⇒ x = 10
The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?- a)10
- b)11
- c)12
- d)13
- e)14
Correct answer is option 'C'. Can you explain this answer?
The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
a)
10
b)
11
c)
12
d)
13
e)
14
|
|
Manasa Kulkarni answered |
Given that, A + B = 12 + B + C
⇒ A - C = 12
Therefore, C is younger than A by 12 years
One year ago, the ratio of Sooraj's and Vimal's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8 . How old is Vimal?- a)32
- b)34
- c)36
- d)38
- e)40
Correct answer is option 'C'. Can you explain this answer?
One year ago, the ratio of Sooraj's and Vimal's age was 6 : 7 respectively. Four years hence, this ratio would become 7 : 8 . How old is Vimal?
a)
32
b)
34
c)
36
d)
38
e)
40
|
|
Aarav Sharma answered |
Problem Statement:
One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Solution:
Let's assume that the present age of Sooraj and Vimal is S and V respectively.
Step 1: Formulate equations based on the given information.
- One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively.
(S-1)/(V-1) = 6/7
- Four years hence, this ratio would become 7:8.
(S+4)/(V+4) = 7/8
Step 2: Simplify the equations.
- (S-1)/(V-1) = 6/7
7S-6V = 1
- (S+4)/(V+4) = 7/8
8S-7V = 12
Step 3: Solve for S and V.
- Multiply the first equation by 8 and the second equation by 6.
56S-48V = 8
48S-42V = 72
- Subtract the second equation from the first equation.
8S-6V = -64
- Solve for V.
V = 36
Step 4: Calculate Sooraj's age.
From equation (1),
7S-6V = 1
7S-6(36) = 1
S = 37/7
Step 5: Check the answer.
Four years ago, Sooraj's age was 33 and Vimal's age was 36.
The ratio of their ages was 6:7.
Four years hence, Sooraj's age would be 37 and Vimal's age would be 40.
The ratio of their ages would be 7:8.
Therefore, the answer is option (c) 36.
One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Solution:
Let's assume that the present age of Sooraj and Vimal is S and V respectively.
Step 1: Formulate equations based on the given information.
- One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively.
(S-1)/(V-1) = 6/7
- Four years hence, this ratio would become 7:8.
(S+4)/(V+4) = 7/8
Step 2: Simplify the equations.
- (S-1)/(V-1) = 6/7
7S-6V = 1
- (S+4)/(V+4) = 7/8
8S-7V = 12
Step 3: Solve for S and V.
- Multiply the first equation by 8 and the second equation by 6.
56S-48V = 8
48S-42V = 72
- Subtract the second equation from the first equation.
8S-6V = -64
- Solve for V.
V = 36
Step 4: Calculate Sooraj's age.
From equation (1),
7S-6V = 1
7S-6(36) = 1
S = 37/7
Step 5: Check the answer.
Four years ago, Sooraj's age was 33 and Vimal's age was 36.
The ratio of their ages was 6:7.
Four years hence, Sooraj's age would be 37 and Vimal's age would be 40.
The ratio of their ages would be 7:8.
Therefore, the answer is option (c) 36.
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 agea)4timesb)5timesc)2timesd)3timese)None of theseCorrect 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:
A is as much younger than B and he is older than C. If the sum of the ages of B and C is 50 years, what is definitely the difference between B and A's age?- a)Data inadequate
- b)3 years
- c)2 years
- d)5 years
- e)4 years
Correct answer is option 'A'. Can you explain this answer?
A is as much younger than B and he is older than C. If the sum of the ages of B and C is 50 years, what is definitely the difference between B and A's age?
a)
Data inadequate
b)
3 years
c)
2 years
d)
5 years
e)
4 years
|
|
Prateek Gupta answered |
Age of C < Age of A < Age of B
Given that sum of the ages of B and C is 50 years.
Now we need to find out (B's age - A's age). But this cannot be determined with the given data.
Sobha'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?- a)6 years
- b)5 years
- c)4 years
- d)3 years
- e)7 years
Correct answer is option 'A'. Can you explain this answer?
Sobha'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?
a)
6 years
b)
5 years
c)
4 years
d)
3 years
e)
7 years
|
|
Aarav Sharma answered |
Given information:
- Sobha’s father was 38 years old when she was born.
- Sobha’s mother was 36 years old when her brother, who is four years younger than Sobha, was born.
To find: The difference between the ages of Sobha’s parents.
Let's assume:
Let's assume the age of Sobha's brother is x years.
Therefore, Sobha's age would be x + 4 years.
Difference in the ages of Sobha's parents:
The age difference between Sobha's father and mother would remain constant, regardless of the birth of their children.
Let's calculate:
- Age of Sobha's father when Sobha was born = 38 years
- Age of Sobha's mother when Sobha's brother was born = 36 years
Difference in the ages of Sobha's parents = Age of Sobha's father - Age of Sobha's mother
Substituting the given values:
= 38 years - 36 years
= 2 years
Therefore, the difference between the ages of Sobha's parents is 2 years.
Hence, the correct answer is option (A) 2 years.
- Sobha’s father was 38 years old when she was born.
- Sobha’s mother was 36 years old when her brother, who is four years younger than Sobha, was born.
To find: The difference between the ages of Sobha’s parents.
Let's assume:
Let's assume the age of Sobha's brother is x years.
Therefore, Sobha's age would be x + 4 years.
Difference in the ages of Sobha's parents:
The age difference between Sobha's father and mother would remain constant, regardless of the birth of their children.
Let's calculate:
- Age of Sobha's father when Sobha was born = 38 years
- Age of Sobha's mother when Sobha's brother was born = 36 years
Difference in the ages of Sobha's parents = Age of Sobha's father - Age of Sobha's mother
Substituting the given values:
= 38 years - 36 years
= 2 years
Therefore, the difference between the ages of Sobha's parents is 2 years.
Hence, the correct answer is option (A) 2 years.
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, what was the son's age five years back?- a)20 years
- b)18 years
- c)14 years
- d)22 years
- e)21 years
Correct answer is option 'C'. Can you explain this answer?
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, what was the son's age five years back?
a)
20 years
b)
18 years
c)
14 years
d)
22 years
e)
21 years
|
|
Snehal Banerjee answered |
Let son's present age be x years. Then,
Son's age 5 years back = 19 − 5 = 14
Son's age 5 years back = 19 − 5 = 14
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?
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
|
|
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.
- 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?
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
|
|
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.
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 sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age?- a)23 years
- b)22 years
- c)21 years
- d)20 years
- e)24 years
Correct answer is option 'D'. Can you explain this answer?
The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age?
a)
23 years
b)
22 years
c)
21 years
d)
20 years
e)
24 years
|
|
Prateek Gupta answered |
Let the present age of the son = x Then, present age of the father = ( 60 − x ) Six years ago father's age was 5 times the age of the son
Son's age after 6 years = x + 6 = 14 + 6 = 20
Son's age after 6 years = x + 6 = 14 + 6 = 20
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of the mother?- a)60
- b)50
- c)40
- d)30
- e)45
Correct answer is option 'C'. Can you explain this answer?
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. What is the present age of the mother?
a)
60
b)
50
c)
40
d)
30
e)
45
|
|
Chirag Sen answered |
Let present age of the person =x
Then, present age of the mother = 5x/2
Given that, after 8 years, the person will be one-half of the age of his mother.
Then, present age of the mother = 5x/2
Given that, after 8 years, the person will be one-half of the age of his mother.
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?
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
|
|
Snehal Banerjee answered |
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
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:- a)14 years
- b)18 years
- c)20 years
- d)22 years
Correct answer is option 'D'. Can you explain this answer?
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
a)
14 years
b)
18 years
c)
20 years
d)
22 years
|
Target Study Academy answered |
Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.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?
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
|
|
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
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?
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
|
|
Devika Yadav answered |
Let age of the son before 8 years = x
Then, age of Kamal before 8 years ago = 4x
After 8 years, Kamal will be twice as old as his son
⇒ 4 x + 16 = 2 ( x + 16 )
⇒ x = 8
Present age of Kamal = 4 x + 8 = 4 × 8 + 8 = 40
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?
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
|
|
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)
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)
A man's age is 125% of what it was 10 years ago, but 
of what it will be after 10years. What is his present age?
- a)70
- b)60
- c)50
- d)40
- e)45
Correct answer is option 'C'. Can you explain this answer?
A man's age is 125% of what it was 10 years ago, but of what it will be after 10years. What is his present age?
of what it will be after 10years. What is his present age?a)
70
b)
60
c)
50
d)
40
e)
45
|
|
Arnab Kumar answered |
Let the age before 10 years =x. Then,
Present age = x+10=40+10=50
Present age = x+10=40+10=50
Chapter doubts & questions for Problems on Age - General Test Preparation for CUET UG 2025 is part of CUET Commerce exam preparation. The chapters have been prepared according to the CUET Commerce exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CUET Commerce 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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