Question

Tanushri and anushri's 2years age ratio is 5 : 6. Today there age ratio is 6 : 7, then tanushri's age is ?​

Answer 1

Answer:

Tanushri's age is 10 years.

Explanation :

Question says that,

2 years ago the age ratio of Tanushri and Anushri was 5 : 6. Their present age ratio is 6 : 7

Find Tanushri's age.

Let's say 2 years ago the age of :

• Tanushri = $5x$
• Anushri = $6x$

2 years hence, age of :

• Tanushri = $(5x + 2)$ years.
• Anushri = $(6x + 2)$ years.

Given,

$\implies (5x + 2) : (6x + 2) = 6 : 7$

Solving for $\boldsymbol x$ :

$\implies \dfrac{(5x + 2)}{(6x + 2)} = \dfrac{6}{7}$

$\implies 7(5x + 2) = 6(6x + 2)$

$\implies 35x + 14 = 36x + 12$

$\implies 14 - 12 = 36x - 35x$

$\implies 2 = x$

${ \therefore{ \sf{The \: value \: of {\boldsymbol{x}} \: is \: 2 \: years}}}$

Hence, Tanushri's age is :

• $5x = \bf 5(2) = 10\: years.$

Answer 2

Given -

• The ration of Tanusri and Anushri 2yrs ago was 5 : 6

• Present ratio of their ages is 6 : 7

To find -

• Age of Tanushri

Solution -

In the question, we are provided with the ratio of ages of Tanushri and Anushri, 2yrs back, and the present ratio of their ages, and we need to find the age of Tanushri, for that, first we will take a common ratio x, after that, we will write them in rational form, then will do cross multiplication, then we will solve the further question.

Let -

The the common ratio be x

So -

Tanushri's age = 5 = 5x

Anushri's age = 6 = 6x

2 years ago -

Tanushri's age = 5x = 5x + 2

Anushri's age = 6x = 6x + 2

So -

$\bf \longrightarrow \: \dfrac{5x \: + \: 2}{6x \: + \: 2}$

Their present ages -

$\bf \longrightarrow \dfrac{6}{7}$

Making a linear equation -

$\bf \longrightarrow \: \dfrac{5x \: + \: 2}{6x \: + \: 2} = \: \dfrac{6}{7} \\ \\ \sf \: \: \: (after \: cross \: multiplication) \\ \\ \bf \longrightarrow \: 7(5x \: + \: 2) \: = 6(6x \: + \: 2) \\ \\ \bf \longrightarrow \: 35x \: + \: 14 \: = 36x \: + \: 12 \\ \\ \bf \longrightarrow \: 35x\: - \: 36x\: =\: 12\: -\: 14 \\ \\ \bf \longrightarrow\: \cancel{-}x\: =\: \cancel{-}2 \\ \\ \bf \longrightarrow\: x\: =\: 2$

Now -

We will find Tanushri's age by multiplying, 5 with 2.

$\bf \longrightarrow \: 5x \\ \\ \bf \longrightarrow \: 5 \: \times \: 2 \: = 10 \: yrs$

$\therefore$ Tanushri's age is 10 years.

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