**Ages Problems**

Hello Readers

Today we will discuss Ages Problems

Ages Problems are generally asked in most of the competitive examinations. To solve **Ages Problems** , the knowledge of linear equations is essential. In such problems, there may be three situations –

(i) Age some year ago (Before)

(ii) Present age

(iii) Age some year hence (After)

Let’s start discussing the topic – Ages Problems with the help of some Examples-

**Example 1**

The ratio of present age of A and B is 2:3. The present age of A is 20 years. Find the age of B after 5 years.

**Solution –** Let the age of A is 2x years and age of B is 3x years.

2x = 20, x = 10

Then present age of B is

3x = 3 × 10 = 30 years.

After 5 years,

Age of B = 30 + 5 = 35 years

**Trick**

A^{0 }+ B^{0 }= 2:3

A^{0 }= 20 years.

B^{0 }= 20/2 × 3 = 30 years.

B^{+5 }= 30 + 5 = 35 years.

**Example – 2**

The present ratio of age of A and B is 3:5. If the sum of the age of A and B is 48 years. Find the ages of A and B before 5 years.

**Solution –**

Let the ages of A and B are 3x years and 5x years respectively.

3x + 5x = 48

8x = 48

x = 48/8 = 6 years

Then the present age of B is

= 3 × x = 3 × 6 = 18 years.

Before 5 years, the age of A is

18 – 5 = 13 years.

Then the present age of B is

= 5 × x = 5 × 6 = 30 years.

Before 5 years the age of B.

30 – 5 = 25 years.

**Trick**

A^{0 }+ B^{0 }= 3:5

(A^{0 }+ B^{0}) = 48 years

A^{-5 }=?

B^{-5}=?

A^{0 }= 48/8 × 3 = 18 years

^{ }A^{-5 }= 18 – 5 = 13 years

B^{0} = 48/8 × 5 = 30 years

B^{-5} = 30 – 5 = 25 years.

**Example 3**

The ratio of ages of A and B before 5 year was 2:3. If the sum of ages of A and Bat present is 45 years. Find the present ages of A and B.

**Solution –**

Let the ages of A and b is 5 years before are 2x years and 3x years respectively.

Then,

(2x + 5) + (3x + 5) = 45 years

5x + 10 = 45

5x =35

X = 7

The ages of A before 5 years

= 7 × 2 = 14 years

At present age of A

= 14 + 5 = 19 years.

The age of B before 5 years

= 7 × 3 = 21 years

At present age of B

= 21 + 5 = 26 years.

**Trick**

A^{-5 }+ B^{-5 }= 2:3

(A + B) = 45 years

(A + B)^{-5} = 45 – 10 = 35 years

A^{-5 }= 35/5 × 2 = 14 years

A^{0} = 14 + 5 = 19 years

B^{-5 }= 35/5 × 3 = 21 years

B^{0 }= 21+ 5 = 26 years.

**Example – 4**

The ratio of ages of A and B after 5 years will be 3:5. If the sum of ages of A and B at present is 38 years. Find the ages of A and B before 5 years.

**Solution –**

Let the ages of A and B are 3x years and 5x years respectively after 5 years.

Then, (3x – 5) + (5x – 5) = 38 years

8x – 10 = 38 years

8x = 48 years

X = 6 years

The age of A after 5 years

= 6 × 3 = 18 years

Then the age of B after 5 years

= 6 × 5 years = 30 years

The age of A before 5 years

= 18 – 10 = 8 years

The age of B before 5 years

= 30 – 10 = 20 years

**Trick**

A^{+5} – B^{-5} = 3:5

(A + B)^{0} = 38 years

(A + B)^{+5} = 38 + 10 = 48 years

A^{+5} = 48/8 × 3 = 18 years

B^{-5} = 18 – 10 = 8 years

B^{+5} = 48/8 × 5 = 30 years

B^{-5} = 30 – 10 = 20 years

**Example 5**

The present ratio of ages of A and B is 6:7. After 5 years this ratio will be changed to 7:8. Find the present age of A and B.

**Solution –**

Let the present age of A is x years and B is y years.

x/y = 6/7 ———————— (1)

x+5/ y+5 = 7/8 —————– (2)

Solving eq (1) and (2)

We get, x = 30 years

y = 35 years.

**Tricks**

A^{0} : B^{0} = 6:7

A^{+5 }+ B^{+5 }= 7:8

A^{0 }= 5/1 × 6 = 30 years

B^{0 }= 5/1 × 7 = 35 years.

With this we will finish this topic here.

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