Problems on Ages with complete solutions, answers, and tricks to solve

Problem on ages can be categorized into three types, i.e.

(i) Questions based on calculating the present age

(ii) Questions to determine the age of person after k years

(iii) Questions that calculate age of a person before k years.

These three types may cover cases of various types with different combination of ratios, fractions etc.

Note:-

==> If the age of the person is x years then,

Age after k years will be x + k

Age before k years will be x – k

The age k times would be kx

==> If ages are given in form of ratio P: Q then, then P: Q would be Px and Qx respectively.

Given below are various cases of the 3-different type of problems of ages:-

(i) Problems based on present age:

Case 1: Whole number form

The age of mother is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. What is the present age of the daughter and mother?

Formulation of Linear Equations:

Let the age of daughter be x and that of mother will be y. And the first line clearly states that at present the age of mother is thrice of daughter. Therefore, y = 3x.

Now, after 12 years i.e. x + 12, mother’s age after twelve years would be (y + 12) and also it will be twice of her daughter, y + 12 = 2(x + 12).

Final Equations and their solution:

y = 3x , y – 2x = 12

Substituting first equation into second and solving we get, x = 12 years and y = 36

Case 2: Fractional Form

Ravi’s age is 1/6th of her father age. Ravi’s father age will be twice of Vimal age after 10 years. If Vimal’s 8th birthday was celebrated 2 years ago. Then what is the present age of Ravi?

Formulation of Linear Equations:

First, let age of Ravi be x and of his father be y. And it’s Cleary stated that the age of Ravi is 1/6th of his father. Therefore, x = 1/6y.

Now assume Vimal’s age be z, so after 10 years Vimal age would be z+10 and Ravi’s father age will be twice of Vimal. Hence, y+10 = 2(z+10). Also, Vimal was of 8 years 2 years ago. Thus, present age of Vimal = 8 + 2 = 10 = z.

Final Equations and their solution:

x = 1/6y, y + 10 = 2 (z+ 10), z = 10

Substituting z = 10 in 2 equation we can easily get the age of Ravi’s father to be 30 and then we can calculate present age of Ravi. x = 5

Case 3: Combination of Ratio and Fraction form

The ratio between Nirmala and Sathya is 5:6 respectively. If the ratio between 1/3rd age of Nirmala and half of Sathya’s age is 5: 9. Then what will be Sathya’s present age?

Formulation of Linear Equations:

Since, the ratio between Nirmala and Sathya is 5:6. Therefore, their present age would be 5x and 6x respectively. Also, the ratio between 1/3rd age of Nirmala i.e. 1/3 * 5x and half age of Sathya i.e. ½ * 6x is 5:9.

Final Equations and their solution:

5x/3/3x = 5/9

Solving the above equation, we get, 1 = 1

Thus, the present ages cannot be determined with the given information.

(ii) Problems based on age before k years:-

Case 1: Fractional Form

Faritha got married 8 years ago. Today her age is 1 2/7th times her age at the time of her marriage. At present her daughter’s age is 1/6th of her age. What was her daughter’s age 3 years ago?

Formulation of Linear Equations:

Let present age of Farha be x. At present, his age is 9/7th of the age when she got married and it’s been 8 years since she got married. Therefore, her age would be x – 8 when she got married and her present age is 9/7(x – 8). Also, currently her daughter’s age is 1/6th of her. Let the present age of her daughter be y.

Final Equations and their solution:

x = 9/7 * (x – 8), y = x/6

Solving the first equation, we get age of Faritha = 36 years.

Hence her daughter’s present age is 6 years but we need her age 3 years back. So, she would have been 3 years old.

Case 2:

The present age of Ajay and his father are in the ratio 2:5. Four year hence the ratio of their ages becomes 5:11 respectively. What is the father’s age five years ago?

Formulation of Linear Equations:

It’s given in question that the current age of Ajay and his father are in ratio 2:5. Their present age would be 2x and 5x respectively. Four years from now i.e. 2x + 4 and 5x + 4 the ratio between their ages become 5:11

Therefore, five years ago Ajay’s father age = 40 – 5 = 35 years.

(iii) Problems based on age after k years:

Case 1: Whole number form

The sum of present ages of father and son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of father after 4 years?

Formulation of Linear Equations:

Let present age of father, son and mother be x, y and z resp. Since, the sum of the present ages of father and son is 8 years more than the mother i.e. x + y = 8 + z.

Also, mother is 22 years older than son, z = 22 + x. We need to find age of father after 4 years i.e. y + 4

Final Equations and their solution:

x + y = 8 + z, z = 22 + x

Substituting the value of second equation in first we get,

x + y = 8 + 22 + x, y = 30

Therefore, y + 4 = 34 years.

Case 2: Ratio Form

The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

Formulation of Linear Equations:

The ratio between ages of A and B is 6:5. Thus, their present age is 5x and 6x resp. And also, the sum of their ages is 44 i.e. 5x + 6x = 44.

Final Equations and their solution:

6x + 5x = 44, X = 4

But, we need to find the ratio of their ages 8 years from now. Thus, their present ages are 24 and 20 respectively.

After 8 years, their ages will be 32 and 28 and hence, the ratio would be 32:28 i.e. 8:7.

Case 3: Combination of age after k years and before k years.

The ratio between the present ages of A and B is 5:3. The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1. What is the ratio between A’s age 4 years hence and B’s age 4 years ago?

Formulation of Linear Equations:

It’s been given the ratio between the present age of A and B is 5:3. Thus, their present age would be 5x and 3x respectively.

Now, 4 years ago the ratio between A’s age and B’s age 4 years hence is 1:1. The age of A 4 years ago would be 5x – 4 and age of B 4 years from now will be 3x + 4. And the ratio of this is 1:1 i.e. (5x – 4)/ (3x + 4) = 1/1. But we need to calculate the ratio between A and B such that (5x + 4) :(3x – 4)

Final Equations and their solution:

(5x – 4)/ (3x + 4) = 1/1

Solving it we get, x = 4

Hence, A’s current age is 20 and B’s present age is 12. Now putting this value in (5x + 4) :(3x – 4)

TNPSC – PROBLEMS BASED ON AGEProblems based on Age:Problems on Ages with complete solutions, answers, and tricks to solve

Problem on ages can be categorized into three types, i.e.

(i) Questions based on calculating the present age(ii) Questions to determine the age of person after k years(iii) Questions that calculate age of a person before k years.These three types may cover cases of various types with different combination of ratios, fractions etc.

Note:-==> If the age of the person is x years then,

Age after k years will be x + k

Age before k years will be x – k

The age k times would be kx

==> If ages are given in form of ratio P: Q then, then P: Q would be Px and Qx respectively.

Given below are various cases of the 3-different type of problems of ages:-(i) Problems based on present age:Case 1: Whole number formThe age of mother is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. What is the present age of the daughter and mother?

Formulation of Linear Equations:Let the age of daughter be x and that of mother will be y. And the first line clearly states that at present the age of mother is thrice of daughter. Therefore, y = 3x.

Now, after 12 years i.e. x + 12, mother’s age after twelve years would be (y + 12) and also it will be twice of her daughter, y + 12 = 2(x + 12).

Final Equations and their solution:y = 3x , y – 2x = 12

Substituting first equation into second and solving we get, x = 12 years and y = 36

Case 2: Fractional FormRavi’s age is 1/6th of her father age. Ravi’s father age will be twice of Vimal age after 10 years. If Vimal’s 8th birthday was celebrated 2 years ago. Then what is the present age of Ravi?

Formulation of Linear Equations:First, let age of Ravi be x and of his father be y. And it’s Cleary stated that the age of Ravi is 1/6th of his father. Therefore, x = 1/6y.

Now assume Vimal’s age be z, so after 10 years Vimal age would be z+10 and Ravi’s father age will be twice of Vimal. Hence, y+10 = 2(z+10). Also, Vimal was of 8 years 2 years ago. Thus, present age of Vimal = 8 + 2 = 10 = z.

Final Equations and their solution:x = 1/6y, y + 10 = 2 (z+ 10), z = 10

Substituting z = 10 in 2 equation we can easily get the age of Ravi’s father to be 30 and then we can calculate present age of Ravi. x = 5

Case 3: Combination of Ratio and Fraction formThe ratio between Nirmala and Sathya is 5:6 respectively. If the ratio between 1/3rd age of Nirmala and half of Sathya’s age is 5: 9. Then what will be Sathya’s present age?

Formulation of Linear Equations:Since, the ratio between Nirmala and Sathya is 5:6. Therefore, their present age would be 5x and 6x respectively. Also, the ratio between 1/3rd age of Nirmala i.e. 1/3 * 5x and half age of Sathya i.e. ½ * 6x is 5:9.

Final Equations and their solution:5x/3/3x = 5/9

Solving the above equation, we get, 1 = 1

Thus, the present ages cannot be determined with the given information.

(ii) Problems based on age before k years:-Case 1: Fractional FormFaritha got married 8 years ago. Today her age is 1 2/7th times her age at the time of her marriage. At present her daughter’s age is 1/6th of her age. What was her daughter’s age 3 years ago?

Formulation of Linear Equations:Let present age of Farha be x. At present, his age is 9/7th of the age when she got married and it’s been 8 years since she got married. Therefore, her age would be x – 8 when she got married and her present age is 9/7(x – 8). Also, currently her daughter’s age is 1/6th of her. Let the present age of her daughter be y.

Final Equations and their solution:x = 9/7 * (x – 8), y = x/6

Solving the first equation, we get age of Faritha = 36 years.

Hence her daughter’s present age is 6 years but we need her age 3 years back. So, she would have been 3 years old.

Case 2:The present age of Ajay and his father are in the ratio 2:5. Four year hence the ratio of their ages becomes 5:11 respectively. What is the father’s age five years ago?

Formulation of Linear Equations:It’s given in question that the current age of Ajay and his father are in ratio 2:5. Their present age would be 2x and 5x respectively. Four years from now i.e. 2x + 4 and 5x + 4 the ratio between their ages become 5:11

Final Equations and their solution:(2x + 4)/ 5 = (5x + 4) / 11, 22x + 44 = 25x + 20, X = 8

Age of Ajay and his father is 16 and 40 resp.

Therefore, five years ago Ajay’s father age = 40 – 5 = 35 years.

(iii) Problems based on age after k years:Case 1: Whole number formThe sum of present ages of father and son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of father after 4 years?

Formulation of Linear Equations:Let present age of father, son and mother be x, y and z resp. Since, the sum of the present ages of father and son is 8 years more than the mother i.e. x + y = 8 + z.

Also, mother is 22 years older than son, z = 22 + x. We need to find age of father after 4 years i.e. y + 4

Final Equations and their solution:x + y = 8 + z, z = 22 + x

Substituting the value of second equation in first we get,

x + y = 8 + 22 + x, y = 30

Therefore, y + 4 = 34 years.

Case 2: Ratio FormThe ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

Formulation of Linear Equations:The ratio between ages of A and B is 6:5. Thus, their present age is 5x and 6x resp. And also, the sum of their ages is 44 i.e. 5x + 6x = 44.

Final Equations and their solution:6x + 5x = 44, X = 4

But, we need to find the ratio of their ages 8 years from now. Thus, their present ages are 24 and 20 respectively.

After 8 years, their ages will be 32 and 28 and hence, the ratio would be 32:28 i.e. 8:7.

Case 3: Combination of age after k years and before k years.The ratio between the present ages of A and B is 5:3. The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1. What is the ratio between A’s age 4 years hence and B’s age 4 years ago?

Formulation of Linear Equations:It’s been given the ratio between the present age of A and B is 5:3. Thus, their present age would be 5x and 3x respectively.

Now, 4 years ago the ratio between A’s age and B’s age 4 years hence is 1:1. The age of A 4 years ago would be 5x – 4 and age of B 4 years from now will be 3x + 4. And the ratio of this is 1:1 i.e. (5x – 4)/ (3x + 4) = 1/1. But we need to calculate the ratio between A and B such that (5x + 4) :(3x – 4)

Final Equations and their solution:(5x – 4)/ (3x + 4) = 1/1

Solving it we get, x = 4

Hence, A’s current age is 20 and B’s present age is 12. Now putting this value in (5x + 4) :(3x – 4)

We get, 24:8 = 3:1

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