## Formulas and Quick Tricks for Age Problems

- If the current age is x, then n times the age is nx.
- If the current age is x, then age n years later/hence = x + n.
- If the current age is x, then age n years ago = x – n.
- The ages in a ratio a : b will be ax and bx.
- If the current age is x, then 1/n of the age is x/n

### Sample Questions – Problems on Ages

The more questions a candidate solves, he is more likely to understand the concept and increase their speed in answering the age problems quickly without making mistakes.

Thus, to help candidates, given below are a few sample Problems on Ages questions along with their solution.

**Q 1.** The present age of Aradhana and Aadrika is in the ratio 3:4. 5 years back, the ratio of their ages was 2:3. What is the present age of Aradhana?

- 12 years
- 15 years
- 20 years
- 22 years
- 10 years

**Answer: (2) 15 years**

**Solution:**

Let the present age of Aradhana be 3x

Let the present age of Aadrika be 4x

5 years back, Aradhana’s age = (3x-5) years

5 years back, Aadrika’s age = (4x-5)

According to the question, (3x-5) : (4x-5) = 2:3

⇒(3x-5) ÷ (4x-5) = 2/3

⇒3(3x-5) = 2(4x-5)

⇒9x-15 = 8x-10

⇒x = 5

Therefore, Aradhana’s current age = 3×5 = 15 years

**Q 2. **If the total ages of Iqbal and Shikhar is 12 years more than the total age of Shikhar and Charu. Charu is how many years younger than Iqbal?

- 11 years
- 13 years
- 15 years
- None of the above
- Cannot be Determined

**Answer: (4) None of the Above**

**Solution:**

Let the age of Iqbal be x

Let the age of Shikhar be y

Let the age of Charu be z

Then, according to question,

(x+y) – (y+z) = 12

⇒x+y-y-z = 12

⇒x-z = 12

Thus, Charu is 12 years younger than Iqbal

**Q 3.** A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?

- 40 years
- 32 years
- 33 years
- 45 years
- 22 years

**Answer: (4) 45 years**

**Solution:**

Let the present age of the father be 2x

So, the present age of the daughter = x

According to the question,

⇒2x-20 = 10(x-20)

⇒2x-20 = 10x – 200

⇒8x = 180

⇒x= 22.5

Thus, the present age of father = 22.5 × 2 = 45 years

**Q 4.** Arun is 2 years older than Bharat who is twice as old as Charat. If the total of the ages of Arun, Bharat and Charat be 27, then how old is Bharat?

- 10 years
- 12 years
- 15 years
- 13 years
- 11 years

**Answer: (1) 10 years**

**Solution:**

Let the present age of Charat be x

So, Bharat’s present age = 2x

And Arun’s present age = 2+2x

According to the question,

x+2x+2+2x = 27

⇒5x+2 = 27

⇒5x=25

⇒x=5

So, Bharat’s age = 2×5 = 10 years

**Q 5. **The sum of the ages of a daughter and mother is 56 years; after four years the age of the mother will be three times that of the daughter. What is the age of the daughter and the mother, respectively?

- 12 years, 41 years
- 12 years, 30 years
- 11 years, 34 years
- 12 years, 44 years
- 21 years, 42 years

**Answer: (4) 12 years, 44 years**

**Solution:**

Let the present age of the mother be x years and the present age of the daughter be y years

According to the question, x+y = 56 —- (1)

After 4 years, age of the Mother = x+4

Age of the daughter after 4 years = y+4

So,

x+4 = 3 (y+4) —- (2)

x+4 = 3y + 12

From the equation (1) we get, x = 56-y

Thus, keep the value of x in equation 2, we get

(56-y) + 4 = 3y + 12

⇒60 – y = 3y + 12

⇒y = 12

So, the daughter’s present age is 12 years

Mother’s present age = 56-12 = 44 years