Question

The present age of Manju is four times the present age of her sister Mala.
After 10 years twice Manju's age will be four times Mala's age. Find their
present ages.​

Answer 1

Answer:-

Let the present age of Mala be x years and Manju be y years.

Given:

Manju's age is four times the present age of Mala.

→ y = 4x -- equation(1).

And,

After 10 years ,

Twice the age of Manju = Four times the age of Mala .

→ 2*(Manju's age after 10 years) = 4*(Age of Mala after 10 years)

→ 2*(y + 10) = 4(x + 10)

→ 2y + 20 = 4x + 40

→ 2y - 4x = 40 - 20

→ 2(y - 2x) = 20

Substitute the value of y from equation (1).

→ 4x - 2x = 20/2

→ 2x = 10

→ x = 10/2

→ x = 5

→ Present age of Mala (x) = 5 years.

→ Present age of Manju (y) = 4x = 4(5) = 20 years.

Answer 2

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{ANSWER}}}}⋆$

• Present age of Mala = 5 years.
• Present age of Manju = 20 years.

$\huge{\bold{\star{\fcolorbox{black}{lightgreen}{EXPLANATION}}}}⋆</p><p>$

$\blue{\bold{\underline{\underline{Let}}}}$

• Present age of Mala = x years.
• Present age of Manju = y years.

$\blue{\bold{\underline{\underline{Given}}}}$

• Manju is four times the present age of her sister Mala.

=> y = 4x ----------- (i)

$\blue{\bold{\underline{\underline{And}}}}$

• After 10 years twice Manju's age will be four times Mala's age.

2(Manju's age after 10 years) = 4(Mala's age after 10 year)

2(y + 10) = 4(x + 10)

=> 2y + 20 = 4x + 40

=> 2y - 4x = 40 - 20

=> 2(y - 2x) = 20

$\blue{\bold{\underline{\underline{Substitute \: the \: value \: of \: y \: from \: equation \: (i)}}}}$

4x - 2x = 20/2

=> 2x = 10

=> x = 10/2

=> x = 5

$\blue{\bold{\underline{\underline{ANSWER}}}}$

Present age of Mala = 5 years

Present age of Manju = 4x

= 4(5)

= 20 years.