Ages Questions & Answers (maths)

 Ages Questions & Answers

(Maths)

Q.1: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

i) 4 years

ii) 8 years

iii) 10 years

iv) None of these

Ans: i) 4 years 

Let's denote the age of the youngest child as "x". The ages of the other children can be represented as x + 3, x + 6, x + 9, and x + 12.

The sum of their ages is given as 50:

x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

Simplifying the equation:

5x + 30 = 50

5x = 20

x = 4

So, the age of the youngest child is 4 years old.

Q.2: Father is four times the age of his daughter. If after 5 years, he would be three times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?

i) 1

ii) 2

iii) 3

iv) 4

Ans: iii) 3

Let's denote the daughter's current age as "d" and the father's current age as "f".

Given that the father is four times the age of his daughter: f = 4d

After 5 years, the father's age will be "f + 5" and the daughter's age will be "d + 5". It's also given that the father's age will be three times his daughter's age at that time: 

f + 5 = 3(d + 5)

Substituting the first equation (f = 4d) into the second equation: 

4d + 5 = 3(d + 5) 4d + 5 = 3d + 15 d = 10

So, the daughter's current age is 10 years old, and the father's current age is 4 times that, which is 40 years old.

After 5 more years, the father will be 45 years old and the daughter will be 15 years old. 

The ratio of their ages would be 45/15 = 3.

Therefore, the father would be three times the age of his daughter 5 years from now.

Q.3: Ram is younger than Rahim by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Ram ?

i) 18

ii) 20

iii) 22

iv) 24.5

Ans: iv) 24.5

Let's denote Ram's age as "r" and Rahim's age as "h".

Given that Ram is younger than Rahim by 7 years:

h - r = 7

Also, their ages are in the ratio of 7 : 9:

r/h = 7/9

We have two equations:

h - r = 7     ------- (i)

r/h = 7/9  -------(ii)     

From the second equation, we can express "h" in terms of "r":

h = (9/7) * r

Substitute the value of "h" from the second equation into the first equation:

(9/7) * r - r = 7

Simplify the equation:

(2/7) * r = 7

=> r = 7 * (7/2)

=> r = 24.5

So, Ram is approximately 24.5 years old.

Q. 4:  Riya'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?

i) 2 years

ii) 3 years

iii) 5 years

iv) 6 years

Ans: iv) 6 years

Let's denote Riya's current age as "r", her brother's age as "b", her father's age as "f", and her mother's age as "m".

We have the following information:

a) Riya's father was 38 years old when she was born: f - r = 38

b) Riya's mother was 36 years old when her brother was born: m - b = 36

c) Riya's brother is four years younger than her: b = r - 4

From the third piece of information, we can substitute the value of "b" in the second equation:

m - (r - 4) = 36

m - r + 4 = 36

m - r = 32

Now we have two equations:

f - r = 38 ------ (i)

m - r = 32 ------(ii)

Subtract the second equation from the first equation to find the difference between the ages of Riya's parents:

(f - r) - (m - r) = 38 - 32

f - m = 6

So, the difference between the ages of Riya's parents is 6 years.

Q. 5: The average age of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace A, the average would be 21. The ages of A, B and C respectively are:

i) 18,22,20

ii) 18,20,22

iii) 22,18,20

iv) 22,20,18

Ans: iii) 22,18,20

Let's denote the ages of A, B, and C as "age_A," "age_B," and "age_C" respectively.

Given that the average age of A and B is 20 years, we can write the equation: 

(age_A + age_B) / 2 = 20.

Similarly, if C were to replace A, the average would be 19, so we have: 

(age_C + age_B) / 2 = 19.

And if C were to replace B, the average would be 21, so we have: 

(age_A + age_C) / 2 = 21.

Now we have a system of three equations with three unknowns. By solving this system, we can find the ages of A, B, and C.

From the first equation, we can express age_B in terms of age_A: age_B = 40 - age_A.

Substitute this expression for age_B into the second equation: (age_C + 40 - age_A) / 2 = 19.

Simplify the equation: age_C + 40 - age_A = 38.

From the third equation, we can express age_C in terms of age_A: age_C = 42 - age_A.

Substitute this expression for age_C into the simplified second equation: 42 - age_A + 40 - age_A = 38.

Combine like terms: 82 - 2 * age_A = 38.

Solve for age_A: age_A = (82 - 38) / 2 = 22.

Now that we know age_A is 22, we can find age_B using the first equation: age_B = 40 - age_A = 40 - 22 = 18.

And finally, age_C can be found using the third equation: age_C = 42 - age_A = 42 - 22 = 20.

So, the ages of A, B, and C are 22 years, 18 years, and 20 years respectively.

Q. 6:  A and b are 50 and 70 years old how many years ago was ratio of their ages 2:3

i) 10 years

ii) 12 years

iii) 13 years

iv) 15 years

Ans: i) 10 years 

Let's denote the number of years ago as "x" when the ratio of their ages was 2:3.

So, "x" years ago, A's age was 50 - x, and B's age was 70 - x.

According to the given information, the ratio of their ages "x" years ago was 2:3:

(50 - x) / (70 - x) = 2 / 3.

Now, cross-multiply to solve for "x":

3 * (50 - x) = 2 * (70 - x).

150 - 3x = 140 - 2x.

Now, solve for "x":

x = 10.

So, the ratio of their ages was 2:3, 10 years ago.