Question

the ratio of present ages of Sudha and Nita is 6:7. five years ago the ratio of their ages was 5:6. what is Sudha present age​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer}}}}$

The present age of Sudha is 30 years and Nita is 35 years.

$\mathfrak{\large{\underline{\underline{Explanation :- }}}}$

$\textbf{Given :}$

Present age ratios = 6 : 7

Five years later = 5 : 6

$\textbf{To find :}$

Their present ages

$\textbf{Solution :}$

Consider the Present age of Sudha as 6x

Consider the Present age of Nita as 7x

The Equation formed =

$\boxed{\tt{ \frac{6x - 5}{7x - 5} = \frac{5}{6}}}$

$\tt{\implies} \: \dfrac{6x - 5}{7x - 5} = \dfrac{5}{6}$

$\tt{\implies} \: 6(6x - 5) = 5(7x - 5)$

$\tt{\implies} \: 36x - 30 = 35x - 25$

$\tt{\implies} \: 36x - 35x = - 25 + 30$

$\tt{\implies} \: x = 5$

Value of 6x

$\tt{\implies} \: 6 \times 5 \\ \tt{\implies} \: 30$

Value of 7x

$\tt{\implies} \: 7 \times 5 \\ \tt{\implies} \: 35$

$\therefore$ The present age of Sudha is 30 years and Nita is 35 years.

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\tt{\implies} \: 6(30 - 5) = 5(35 - 5) \\ \tt{\implies} \:180 - 30 = 175 - 25 \\ \tt{\implies} \: 150 = 150$

$\therefore$ The present age of Sudha is 30 years and Nita is 35 years.

Answer 2

Answer:

Sudha's present age is 30

Step-by-step explanation:

• The ratio of present ages of Sudha and Nita is 6:7.

• let the common factor of  ratio be x.

        So the Present age of Sudha is 6x and present age of  Nita is 7x.

• 5 years back , Sudha's age was 6x-5 , Nita's age was 7x-5

  ratio of their age was (6x-5):(7x-5)= 5:6

   so, $\frac{6x-5}{7x-5}$ = $\frac{5}{6}$

⇒ 36x - 30 = 35x - 25

⇒ 36x - 35x = 30 - 25

⇒ x = 5

Hence, Sudha's present age = 6x = 6×5 = 30