Question

Arvind is eight years older than his sister in three years he will be twice as old as sister how old are they now ​

Answer 1

Answer: He is 13 years old and his sister is 5 years old.

Step-by-step explanation:

We can assume Arvind's age to be 'x' years

⇒ His sister's age is  = x-8 years

According to the question,

x+3 = [(x-8)+3] × 2

{because in three years' time he'll be twice her age}

Solving the equation,

x+3 = [x-5] × 2

x+3 = 2x - 10

Transposing,

2x-x = 13

x = 13 {hence, proved}

Answer 2

Answer:

Arvind is 13 years old and his sister is 5 Years old.

Step-by-step explanation:

Gívєn -

Arvind is = eight years older than his sister

Three years hence he will be twice as old as sister.

Tσ fínd -

How old are they now

Sσlutíσn -

✯ Let the Present ages be -

• His sister as x
• Arvind as (x + 8)

$\rule{300}{1.5}$

✯ After 3 Years -

• His sister = (x + 3)
• Arvind = (x + 8) + 3

$\rule{300}{1.5}$

✯ According to the Question -

Three years hence he will be twice as old as sister.

$\sf{\implies} \: (x + 8) + 3 = 2(x + 3) \\ \sf{\implies} \:(x + 8) + 3 = 2x + 6 \\ \sf{\implies} \:x + 11 = 2x + 6 \\ \sf{\implies} \:2x - x = 11 - 6 \\ \sf{\implies} \:x = 5$

Present age of his sister = 5 Years

$\rule{300}{1.5}$

Arvind's present age =

$\sf{\implies} \:(x + 8) \\ \sf{\implies} \:(5 + 8) \\ \sf{\implies} \:13$

$\therefore$ Arvind is 13 years old and his sister is 5 Years old.