Question

The sum of Present ages of father and his son is 60 years. Six

years ago, the age of father was five times the age of son. Find thepresent age of father and son​

Answer 1

Answer:

Son is 14 years old and Father is 46 years old.

Step-by-step explanation:

Sum of their ages = 60 years

6 years ago, father = 5 times his son

Let their present ages be -

• Son as x
• Father as y

According to the first condition,

$\longrightarrow$ x + y = 60

$\longrightarrow$ x = 60 – y ----- (Equation 1)

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Ages 6 years ago,

• Son = x – 6
• Father = y – 6

According to the second condition,

$\longrightarrow$ (y – 6) = 5(x – 6)

$\longrightarrow$ y – 6 = 5x – 30 ----- (Equation 2)

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Substitute equation 1 in equation 2,

$\longrightarrow$ y – 6 = 5(60 – y) – 30

$\longrightarrow$ y – 6 = 300 – 5y – 30

$\longrightarrow$ y – 6 = 270 – 5y

$\longrightarrow$ y + 5y = 270 + 6

$\longrightarrow$ 6y = 276

$\longrightarrow$ y = 276/6

$\longrightarrow$ y = 46

Father's present age = 46 years

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★ Son's age :

Substitute value of y in equation 1

$\longrightarrow$ x = 60 – 46

$\longrightarrow$ x = 14

Son's present age = 14 years

Therefore, Son is 14 years old and Father is 46 years old.

Answer 2

Answer

» We are given with the sum of the present ages of the father and his son. We are also given that six years ago the father was five times greater than his son.

Sum of ages before six years :

${\sf \dashrightarrow 60 - (6 + 6)}$

${\sf \dashrightarrow 60 - 12}$

${\sf \dashrightarrow 48}$

Now, let's find the age of son.

Let the age of son be x.

Let the age of father be 5x.

Age of son (6 years ago) :

${\sf \dashrightarrow x + 5x = 48}$

${\sf \dashrightarrow 6x = 48}$

${\sf \dashrightarrow x = \dfrac{48}{6} = 8}$

Age of father (6 years ago) :

${\sf \dashrightarrow 5x = 5(8)}$

${\sf \dashrightarrow 40}$

Now, let's find the present ages of father and son.

Present age of father :

${\sf \dashrightarrow 40 + 6}$

${\sf \dashrightarrow 46 \: years}$

Present age of son :

${\sf \dashrightarrow 8 + 6}$

${\sf \dashrightarrow 14 \: years}$

Hence, the present ages of father and son are 46 and 14 respectively.