Question

Sumit is 3 times as old his son. Five year later he shall we two and a half times as old as his son. How old is sumit at present?​

Answer 1

✬ Son = 15 Years ✬

✬ Sumit = 45 Years ✬

Step-by-step explanation:

Given:

• Sumit is 3 times as old as his son.
• After 5 years his age will be 2(1/2) as old as his son.

To Find:

• What is the present age of sumit ?

Solution: Let the age of Sumit's son be x years. Therefore,

➼ Sumit's age = 3 times of x

➼ Sumit's age = 3x years.

[ After 5 year their ages will be ]

• Son age = (x + 5) years
• Sumit's age = (3x + 5) years

A/q

• After 5 years sumit's age will be 2(1/2) as old as his son.

$\implies{\rm }$ (3x + 5) = 2(1/2) × (x + 5)

$\implies{\rm }$ 3x + 5 = 5/2(x + 5)

$\implies{\rm }$ 3x + 5 = 5x + 25/2

$\implies{\rm }$ 2(3x + 5) = 5x + 25

$\implies{\rm }$ 6x + 10 = 5x + 25

$\implies{\rm }$ 6x – 5x = 25 – 10

$\implies{\rm }$ x = 15

So present age of

➮ Son age is x = 15 years

➮ Sumit's age is 3(15) = 45 years

Answer 2

Given :-

• Sumit is 3 times as old his son
• Five year later he shall we 2½ times as old as his son

To Find :-

• Present age of Sumit

Solution :-

Let the age of Sumit's son be ‘x’

$\sf\therefore Sumit's \: age = 3x$

★ After 5 years :-

• Son age = (x + 5)
• Sumit's age = (3x + 5)

A. T. Q :-

We have,

• Five year later he shall we 2½ times as old as his son

$:\implies\sf3x + 5 = 2\frac{1}{2} \times x + 5$

$:\implies\sf3x + 5 = \frac{5}{2} \times x + 5$

$:\implies\sf3x + 5 = 5x + \frac{25}{2}$

$:\implies\sf2(3x + 5) = 5x + 25$

$:\implies\sf6x + 10 = 5x + 25$

$:\implies\sf6x - 5x = 25 - 10$

$:\implies\underline{\boxed{\blue{\sf x = 15}}}$

$\green{\therefore\underline{\sf Sumit's\:age = 3x = 3 \times 15 = 45years}}$