### Important Formulas For **Age-Related Questions**

Below are a few formulas linked to ages problems that may help you answer the questions faster and gain a better understanding of the concept:

- If you assume that you are currently x years old, you will be (x+n) years old after n years.
- If you assume the present age is x, the age before n years is (x-n).
- If the age is expressed as a ratio, such as p:q, the age should be interpreted as qx and px.
- If you assume the current age to be x, the current age will be (xn) years multiplied by n.
- If you assume that your present age is x, then 1/n of your age is (x/n) years.

### Tips and Tricks to Solve Problems on Ages

Candidates who are unfamiliar with the subject and frequently skip or incorrectly answer the age problems should refer to the guidelines provided below. These pointers may assist you in systematically answering the question and then determining the answer.

- The most important thing is to attentively study the question and gradually build the equation that will assist you in answering it.
- Basic operations such as addition, subtraction, multiplication, and division will aid a candidate in arriving at the correct answer, and no difficult computations are necessary to do so.
- Arrange the values provided by accurately placing them in an equation and assigning variables to the unknown values.
- To find the solution, solve the equation once it has been generated.
- The final step is to double-check the result by plugging it into the equation to confirm that no errors were made throughout the calculation.

**Have a look at the following Age-Related questions:**

**Question. 1: ****The present ages of R and S are in the ratio 7:6. Nine years from now, the age of R would be double S’s age 3 years ago. What is the present age of S?**

**Solution:**

Let the present ages of R and S be R and S years, respectively.

R/S= 7/6 ⇒ 6R = 7S…..(1)

(R + 9)/(S - 3) = 2 ⇒ R + 9 = 2S – 6 ⇒ 2S – R = 15…..(2)

Solving equations (1) and (2)

R = 21 S = 18

**Question. 2: **The ratio of the present ages of A to B is 2:3. Four years hence, the ratio of their ages will be 5:7. What is the present age of A?

**Solution: **Let the present ages of A and B be 2*x* and 3*x* respectively. Therefore,

After 4 years,

A’s age = (2*x* + 4) years

B’s age = (3*x* + 4) years

Therefore,

2x + 4 / 3x + 4 = 5/7

7(2x + 4) = 5(3x + 4)

14x + 28 = 15x + 20

x = 8

Thus, A’s present age = 8 × 2 = 16 years

**Question. 3: **Ram’s mother was 4 times as old as Ram 12 years ago. After 12 years, she will twice as old as Ram. What is the present age of Ram’s mother?

**Solution:**

Let, the present age of Ram = x and present age of his mother = y

Ram’s mother was 4 times as old as Ram 12 years ago.

According to problem,

⇒y – 12 = 4(x – 12)

⇒y = 4x – 36 ……… (1)

After 12 years, she will twice as old as Ram.

According to problem,

⇒y + 12 = 2(x + 12)

⇒y = 2x + 12 ……… (2)

From (1) and (2) we get,

⇒4x – 36 = 2x + 12

⇒2x = 48

⇒x = 24

Putting the value x= 24 in (2) we get,

⇒y = 2 × 24 + 12

⇒y = 60

∴present age of Ram’s mother = 60 years

**Question. 4: **Vivek said to Ram “I am 3 times as old as you were when I was half of what your age will be 3 years from now”. If the sum of their ages is 50 years, find the age of Ram. (in years).

**Solution:**

Let the present ages of Vivek and Ram be ‘a’ and ‘b’ respectively.

Given, Vivek said to Ram “I am 3 times as old as you were when I was half of what your age will be 3 years from now”.

⇒Vivek’s age = 3 × (Ram’s age when Vivek’s age was half of what Ram’s age will be 3 years from now)

a = 3 X (b - (a - (b + 3)/2)

⇒a = 3b – 3a + 3b/2 + 9/2

⇒4a = 9b/2 + 9/2

⇒8a = 9b + 9

⇒a = (9b + 9)/8

Given, sum of their ages is 50 years.

⇒a + b = 50

⇒(9b + 9)/8 + b = 50

⇒17b + 9 = 400

⇒b = 23 years

**Question. 5: **The sum of the ages of Vidit, Rahul, and Pravin is 93 years. 10 years ago, the ratio of their ages was 2:3:4. What is the present age (in years) of Pravin?

**Solution: **Let their ages 10 years ago be 2z, 3z, and 4z respectively.

Then their present ages will be

Vidit's age = 2z + 10

Rahul's age = 3z + 10

Pravin's age = 4z + 10

Vidit's age + Rahul's age + Pravin's age = (2z + 10) + (3z + 10) + (4z + 10)

Vidit's age + Rahul's age + Pravin's age = 9z + 30

The sum of their present ages is 93.

9z + 30 = 93

9z = 63

z = 7

Therefore, present age of Pravin = 4z + 10 = 4 X 7 + 10 = 38 years

Note: Just try to make two equations and then solve them to get your answer.

**Question 6: **8 years ago, the ratio of the ages of Priyanka and Ritika was 11:17 respectively and 2 years hence, the ratio of their ages will be 8:11. If the ratio of the present ages of Ritika to Manisha is 7:8, what will be the age of Manisha after 3 years?

**Solution**:

Let 8 years ago,

The age of Priyanka = 11x years

The age of Ritika = 17x years

According to the question,

11x+10/17x+10 = 8/11

⇒ 121x + 110 = 136x + 80

⇒ 15x = 30

⇒ x = 2

Present age of Priyanka = 11 × 2 + 8 = 30 years

Present age of Ritika = 17 × 2 + 8 = 42 years

Present age of Manisha = 42/7 × 8 = 48 years

Required age of Manisha = 48 + 3 = 51 years

The questions given above will help you understand how to form the equations to solve the Age problem questions and what type of questions may be asked from this topic.

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