Question

0-9. Arvind is eight years older than his sister. In three years he will be twice as old as his
sister. How old are they now?​

Answer 1

Given that,

Arvind is 8 yrs older than his sister.

Let the present age of his sister be x.

Therefore his present age = x + 8

ATQ,

After 8 years, Arvind will be twice as old has his sister will be.

➡ (x + 8) + 3 = 2(x + 3)

➡ x + 11 = 2x + 6

➡ x - 2x = 6 - 11

➡ -x = -5

➡ x = 5

Hence, the present ages of :-

• Arvind's sis = x = 5 years

• Arvind = x + 8 = 13 years

VERIFICATION :-

Arvind's age must be twice as his sister's age after 8 years.

LHS :-

» 2(Arvind's sister's age after 3 years)

= 2(5 + 3)

= 2(8)

= 16 years

» Arvind's age after 3 years

= 13 + 3

= 16 years

LHS = RHS. Hence verified!

Answer 2

AnswEr :

☑ Given :

• Arvind is Eight Yrs Old than his Sister.

• In 3 Yrs He will be twice as Old as his Sister.

☑ To Find :

• There Present Age.

☑ Solution :

• Arvind's Sister Present Age = x Yrs
• Arvind's Present Age = (x + 8) Yrs

☢ After 3 Yrs :

» Arvind's Sister Age = (x + 3) Yrs

» Arvind's Age = (x + 8) + 3 = (x + 11) Yrs

☢ A.T.Q.

➟ Arvind's Age = 2 × Arvind's Sister Age

➟ (x + 11) = 2 × (x + 3)

➟ x + 11 = 2x + 6

➟ 11 - 6 = 2x - x

➟ x = 5 Yrs

━━━━━━━━━━━━━━━━━━━━━━━━

▣ Arvind's Sister Age = x Yrs

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 5 Yrs

▣ Arvind's Age = (x + 8) Yrs

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀= (5 + 8) Yrs

⠀⠀⠀⠀⠀⠀⠀⠀= 13 Yrs

$\huge{\red{\ddot{\smile}}}$