Question

1. Rama's mother is five times older than her. After 5 years product of their ages will be 385.
Find present age of Rama.​

Answer 1

Answer:

• The present age of Rama is 6 years.

Step-by-step explanation:

Given that:

• Rama's mother is five times older than her.
• After 5 years product of their ages will be 385.

To Find:

• The present age of Rama.

Let us assume:

• The present age of Rama be x.
• Present of her mother = 5x

After 5 years:

• Rama's age = x + 5
• Her mother's age = 5x + 5

Finding the present age of Rama:

According to the question.

⇢ (x + 5)(5x + 5) = 385

Using distributive law.

⇢ x(5x + 5) + 5(5x + 5) = 385

⇢ 5x² + 5x + 25x + 25 = 385

⇢ 5x² + 30x + 25 - 385 = 0

Solving quadratic equation.

⇢ 5x² + 30x - 360 = 0

Splitting 30x.

⇢ 5x² + 60x - 30x - 360 = 0

⇢ 5x(x + 12) - 30(x + 12) = 0

⇢ (5x - 30)(x + 12) = 0

⇢ (5x - 30) = 0 or (x + 12) = 0

⇢ 5x = 30 or x = - 12

⇢ x = 30/5 or x = - 12

⇢ x = 6 or x = - 12

We know that:

• Age can't be negative.

Therefore,

• The present age of Rama is 6 years.

Answer 2

Answer:

Given :-

• Rama's mother is five times older than her. After 5 years product of their ages will be 385.

To Find :-

• What is the present age of Rama.

Solution :-

Let,

$\mapsto$ Present age of Rama = x years

$\mapsto$ Present age of Rama's mother = 5x

Again 5 years ago :

$\mapsto$ Age of Rama = x + 5 years

$\mapsto$ Age of Rama's mother = 5x + 5

According to the question,

$\implies \sf x + 5 + 5x + 5 =\: 385$

$\implies \sf x(5x + 5) + 5(5x + 5) =\: 385\: \: \bigg\lgroup \bold{By\: using\: Distributive\: Law}\bigg \rgroup$

$\implies \sf 5x^2 + 5x + 25x + 25 =\: 385$

$\implies \sf 5x^2 + 30x + 25 - 385 =\: 0$

$\implies \sf 5x^2 + 30x - 360 =\: 0$

$\implies \sf 5x^2 + (60 - 30)x - 360 =\: 0\: \: \bigg\lgroup \bold{By\: doing\: Middle\: term\: break}\bigg \rgroup$

$\implies \sf 5x^2 + 60x - 30x - 360 =\: 0$

$\implies \sf 5x(x + 12) - 30(x + 12) =\: 0$

$\implies \sf (x + 12)(5x - 30) =\: 0$

$\implies \sf (x + 12) =\: 0$

$\implies \sf x + 12 =\: 0$

$\implies \sf\bold{\purple{x =\: - 12}}\: \bigg\lgroup Age\: can't\: be\: negative\bigg \rgroup$

Either,

$\implies \sf (5x - 30) =\: 0$

$\implies \sf 5x - 30 =\: 0$

$\implies \sf 5x =\: 30$

$\implies \sf x =\: \dfrac{\cancel{30}}{\cancel{5}}$

$\implies \sf\bold{\purple{x =\: 6}}$

Hence, the required age of Rama and Rama's mother are :

$\dashrightarrow$ Present age of Rama :

$\implies \sf x\: years$

$\implies \sf\bold{\red{6\: years}}$

And,

$\dashrightarrow$ Present age of Rama's mother :

$\implies \sf 5x\: years$

$\implies \sf 5(6)\: years$

$\implies \sf 5 \times 6\: years$

$\implies \sf\bold{\red{30\: years}}$

$\therefore$ The present age of Rama is 6 years.