Question

Five years ago, Hemant's age was 7 times the age of his son. Five years
later, his age will be 3 times the age of his son. What are the respective
current ages of Hemant and his son?

a) 40 years and 10 years
b) 35 years and 15 years
с) 45 years and 15 years
d) 45 years and 10 years​

Answer 1

5 years ago:-
Father’s age =y
Son’s age =x
Y=7x
5 years later :-
Father’s age = y+10
Son’s age = x +10
Y+10=3(x+10)
Y+10=3x+30
7x+10=3x+30
4x=20
x=5
Y=5*7=35
Present age :-
Father - 40
Son - 10
Correct option :- (a)

Answer 2

Let :

• Present/ Current age of Hemant = x years
• Present age of son = y years

Given :

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

To find :

Present/current age of Hemant and his son

Solution :

Case 1) 5 years ago

• Hemant's age = x-5
• His son's age = y - 5

Given, 5 years ago , Hemant's age was 7 times the age of his son

➝ (x-5) = 7(y-5)

➝ x - 5 = 7y - 35

➝ x = 7y - 35 + 5

➝ x = 7y - 30 ...... equation 1

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Case 2) 5 years later

• Hemant's age = x+5
• His son's age = y+5

Given, 5 years later, Hemant's age will be 3 times the age of his son.

➝ (x+5) = 3(y+5)

➝ x +5 = 3y + 15

➝ x = 3y + 15-5

➝ x = 3y + 10 ...... equation 2

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Putting value of x from equation 1 into equation 2 we get;

➝ (7y-30) = 3y + 10

➝ 7y - 3y = 10 + 30

➝ 4y = 40

➝ y = 40÷4

➝ y = 10

Now , putting value of y in equation 1, we get;

➝ x = 7(10)-30

➝ x = 70 - 30

➝ x = 40

_______________________________________________

Therefore,

• Hemant's current age = x years = 40 years
• His son's current age = y years = 10 years

ANSWER :

option a) 40 years & 10 years