Question

5 year ago a man was 7 times as old as his son and 5 year hence the father Will be 3 times as old as his son. Find the present age

Answer 1

Given :-

• 5 year ago a man was 7 times as old as his son and 5 year hence the father Will be 3 times as old as his son.

To find :-

• Present ages

Solution :-

Let the present age of man be x then his son's present age be y

• 5 years ago

→ Man's age = x - 5

→ Son's age = y - 5

• x - 5 = 7(y - 5)

→ x - 5 = 7y - 35

→ x - 7y = - 35 + 5

→ x - 7y = - 30 ----(i)

• 5 years hence

→ Man's age = x + 5

→ Son's age = y + 5

• x + 5 = 3(y + 5)

→ x + 5 = 3y + 15

→ x - 3y = 15 - 5

→ x - 3y = 10 -----(ii)

Subtract both the equations

→ (x - 7y) - (x - 3y) = - 30 - 10

→ x - 7y - x + 3y = - 40

→ - 4y = - 40

→ y = 40/4

→ y = 10

Put the value of y in equation (ii)

→ x - 3y = 10

→ x - 3 × 10 = 10

→ x - 30 = 10

→ x = 10 + 30

→ x = 40

Hence,

• Man's present age = x = 10 years

• Son's present age = y = 40 years

Answer 2

Answer:

Step-by-step explanation:

Let’s look at the word equation:

Five years ago, a man was 7 times as old as his son.

Five years hence, father will be three times as old as his son.

Our goal is to find their present ages, and it is easier to multiply than to divide, so let’s use:

S = Son’s present age

M = Man’s present age

Let’s rewrite the sentence to use this detail:

Five years ago, (M–5) was 7 times as old as (S – 5).

Five years hence, (M+5) will be three times as old as (S+5).

Do you see how I turned man and son “five years ago” into (M-5) and (S-5)?

Likewise, man and son “five years hence” became (M+5) and (S+5)

Now let’s turn our revised sentences into equations:

Five years ago, (M–5) was 7 times as old as (S – 5).

M – 5 = 7 (S – 5)

Five years hence, (M+5) will be three times as old as (S+5).

M + 5 = 3 (S + 5)

Let’s get rid of the parentheses, and isolate M by itself on the left of each equation:

M – 5 = 7 (S – 5)

M – 5 = 7S – 35

Add 5 to both sides

M = 7S - 30

M + 5 = 3 (S + 5)

M + 5 = 3S + 15

Subtract 5 from both sides

M = 3S + 10

We now have two equations that are both equal to M:

M = 7S - 30

M = 3S + 10

Since M = M, set these equal to each other

7S – 30 = M = 3S + 10

7S – 30 = 3S + 10

Add 30 to both sides

Subtract 3S from both sides

7S – 3S – 30 + 30 = 3S – 3S + 10 + 30

4S = 40

Divide both sides by 4

S = 10

Go back to either of the M= equations:

M = 7S - 30

M = 7(10) - 30 = 70 - 30 = 40

M = 3S + 10

M = 3(10) + 10 = 30 + 10 = 40

S = 10

M = 40