Question

5 years ago, fathers age was 7 times the age of his son. 5 years later the father's age will be 3 times the age of his son. Find their present age ​

Answer 1

Gɪᴠᴇɴ :-

5 years ago, fathers age was 7 times the age of his son. 5 years later the father's age will be 3 times the age of his son.

ᴛᴏ ғɪɴᴅ :-

• Present age of Son and Father

sᴏʟᴜᴛɪᴏɴ :-

Let present age of son be x years and father's age be y years

then,

✎ According to 1st condition :-

➦ 5 - years ago :-

• Son's age = (x - 5) years
• Father's age = (y - 5)years
• Father's age = 7 × Son's age

➭ (y - 5) = 7( x - 5)

➭ y - 5 = 7x - 35

➭ y = 7x -35 + 5

➭ y = 7x - 30. --(1)

✎ According to 2nd Condition :-

➦ 5 - years later :-

• Son's age = (x + 5) years
• Father's age = (y + 5) years
• Father's age = 3×Son's age

➭ (y + 5) = 3 × (x + 5)

➭ y + 5 = 3x + 15

➭ y = 3x + 15 - 5

➭ y = 3x + 10. ---(2)

From (1) and (2) , we get,

➭ 7x - 30 = 3x + 10

➭ 7x - 3x = 30 + 10

➭ 4x = 40

➭ x = 40/4

➭ x = 10

Put x = 10 in (1) , we get,

➭ y = 7x - 30

➭ y = 7 × 10 - 30

➭ y = 70 - 30

➭ y = 40 years

Hence,

• Son's age = x = 10 years
• Father's age = y = 40 years

Answer 2

Given :

• 5 years ago, fathers age was 7 times the age of his son.

• 5 years later the father's age will be 3 times the age of his son.

To find :

• Their present age =?

Step-by-step explanation :

Let the present age of father's be x years

Then, the present age of son's be y years.

First Case :

After 5 years father’s age = x + 5  

After 5 years ago son’s age = y + 5  

According to the question :

x + 5 = 3(y + 5)

x + 5 = 3y + 15

x - 3y = 15 - 5

x – 3y = 10 .…(i)  

Second Case :

5 years ago father’s age = x – 5  

5 years ago son’s age = y – 5  

According to the question :

x – 5 = 7(y – 5)

x - 5 = 7y - 35

x - 7y = - 35 - 5

x – 7y = -30 ….(ii)

Subtracting (ii) from (i), we get,

x – 3y - (x - 7y) = 10 - (- 30)

x - 3y - x + 7y = 10 + 30

7y - 3y = 10 + 30

4y = 40  

y = 40/4

y = 10  

Therefore, We got the value of, y = 10.

On putting y value in Eq (i), we get,

x – 3y = 10

x – 3 × 10 = 10   [y = 10]

x = 10 + 30

x = 40

Therefore, We got the value of, x = 40

Hence,

The present age of father's, x = 40 years

The present age of the son's, y = 10 years.