Question

two years ago a man was five times as old as his sons two years later his age will be 8 morethan three times the age of the son find the preent age of the man

Answer 1

Answer:

Step-by-step explanation:

Answer 2

✬ Man's age = 42 Years ✬

✬ His son's age = 10 Years ✬

Step-by-step explanation:

Given:

• Two years ago a man was five times as old as his son.
• Two years later his age will be 8 more than three times the age of the son.

To Find:

• Present ages of both .

Solution: Let the present age of man be x years and present age of his son be y years.

• Two years ago their ages was •

• Man's age = (x – 2) Years.
• His son's age = (y – 2) Years.

A/q

$\small\implies{\sf }$ x – 2 = 5 (y – 2)

$\small\implies{\sf }$ x – 2 = 5y – 10

$\small\implies{\sf }$ x = 5y – 10 + 2

$\small\implies{\sf }$ x = 5y – 8..........(1)

• Two years hence their ages will be •

• Man's age = (x + 2) Years.
• His son's age = (y + 2) Years.

A/q

$\small\implies{\sf }$ x + 2 = 8 + 3 (y + 2)

$\small\implies{\sf }$ x + 2 = 8 + 3y + 6

$\small\implies{\sf }$ 5y – 8 + 2 = 8 + 3y + 6 [ From equation 1 ]

$\small\implies{\sf }$ 5y – 6 = 14 + 3y

$\small\implies{\sf }$ 5y – 3y = 14 + 6

$\small\implies{\sf }$ 2y = 20

$\small\implies{\sf }$ y = 20/2

$\small\implies{\sf }$ y = 10

Hence, The present age of his son is y = 10 Years.

∴ Present age of man = x = 5y – 8

→ x = 5 x 10 – 8

→ x = 50 – 8

→ x = 42 Years

Hence, The present age of man is x = 42 Years.