Question

The present ages of Ram and Rahman are in the ratio 8:9 after 5 years the ratio of their ages will be 9:10 find their present ages.
Please give explanation.​

Answer 1

Given : -

The present ages of Ram and Rahman are in the ratio 8 : 9 after 5 years the ratio of their ages will be 9 : 10 .

Required to find : -

• Present ages ?

Solution : -

The present ages of Ram and Rahman are in the ratio 8 : 9 after 5 years the ratio of their ages will be 9 : 10 .

we need to find the present ages of Ram & Rahman .

So,

We should need to use concept related linear equations in 1 variable . In order to solve this question .

Let's consider that ;

Present ages of Ram be x

Present age of Raman be y

According to question ,

It is mentioned that ;

Ths present ages of Ram and Raman are in the ratio of 8 : 9 .

So,

The present age of Ram will be 8x

And present age of Raman will be 9x

Similarly,

After 5 years ,

Age of Ram will be 8x + 5

Age of Raman will be 9x + 5

According to question ,

It is mentioned that ;

After 5 years the ratio of their ages will be 9 : 10 .

This implies ,

8x + 5 : 9x + 5 = 9 : 10

Since,

we know that ;

a : b = a/b

8x +5 / 9x + 5 = 9/10

10 ( 8x + 5 ) = 9 ( 9x + 5)

80x + 50 = 81x + 45

80x - 81x = 45 - 50

- 1 x = - 5

Take - ( minus ) common on both sides

- ( x ) = - ( 5 )

- ( minus ) get's cancelled on both sides

x = 5

Hence,

• Value of x = 5

Substitute this value in the present ages of Ram & Raman .

Hence,

Present age of Ram = 8x = 8(5) = 40 years .

Present age of Raman = 9x = 9(5) = 45 years .

- : Additional Information : -

Question

What is a linear equation in 1 variable ?

Answer

It is an equation which consists of only one variable in it . Here the variable represents one unknown value .

Example :-

2x + 3 = 0 , 3+ 4x = 6 , etc.

Question

What is linear equation in 2 variables ?

Answer

It is an equation which consists of 2 variables in it. Here , the 2 variables represent 2 different values .

Example :-

3x + 4y = 0 , 6x - y = 35 etc.

Note :

Every algebraic expression can become an equation .

But, every equation can't become a algebraic expression.

Same in the case of polynomials too .

Answer 2

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

✴ The present ages of Ram and Rahman are in the ratio 8:9 after 5 years the ratio of their ages will be 9:10 find their present ages.

$\mathbb{\huge{\underline{\green{Answer:-}}}}$

✏ The present age of Ram is 40 yrs & Rehman is 45yrs.

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Given :-

• The present ages of Ram and Rahman are in the ratio 8:9 .

• After 5 years the ratio of their ages will be 9:10

To find :-

• Present age of Ram & Rehman .

Calculation :-

Let the present ages be x

We know, The present ages of Ram and Rahman are in the ratio 8:9 .

So,

• Age of Ram is 8x

• Age of Rehman be is 9x.

According to the question,

After 5 years, the ratio of their ages will be 9:10.

➡ $\dfrac{8x + 5}{9x + 5} = \dfrac{9}{10}$

Applying Cross multiplication rule,

➡ 10(8x + 5) = 9(9x +5)

➡ 80x + 50 = 81x + 45

➡ 81x - 80x = 50 -45

➡ x = 5

We know,

• Age of Ram is 8x

• Age of Rehman be is 9x.

Putting correct value of x,

Present age of Ram = 8x = 8 x 5 = 40 yrs

Present age of Rehman = 9x = 9 x 5 = 45yrs.

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