Question

Sum of the present ages of Manisha and Savita is 31. If 3 years ago age of Manisha was 4 times the age of Savita then find the their present ages​

Answer 1

Answer:

present age of Manisha = 23 years

present age of Savita = 8 years

Answer 2

$\large{\underline{\underline{\mathfrak{\;\;AnswEr\;:}}}}$

• Savita's present age = 8 years
• Manisha's present age = 23 years

$\rule{230px}{.2ex}$

• Question states that the Sum of the present age of Manisha and the present age of Savita is 31 years. Three years ago the age of Manisha was four times the age of Savita. & we're asked to calculate the present age of Manisha and present age of Savita.

Let's say, that the present age of Manisha and Savita be x and y years respectively.

${\underline{\underline{\bigstar\:\textbf{AccordinG to the given QuestiOn :}}}}$

• Sum of the present age of Manisha and Savita is 31 years.

$:\implies\sf x + y = 31$

$:\implies\sf x = 31 - y\qquad\qquad\qquad\qquad\sf\Bigg\lgroup eq_{n}\;(i)\Bigg\rgroup$

• Three years ago the age of Manisha was four times the age of Savita.

» Three years ago,

• Savita's age = (y – 3)
• Manisha's age = (x – 3)

⠀

$\dashrightarrow\sf\quad (x - 3) = 4(y - 3)$

$\dashrightarrow\sf\quad x - 3 = 4y - 12$

$\dashrightarrow\sf\quad x - 4y = -12 + 3$

$\dashrightarrow\sf\quad x - 4y =- 9$

$\dashrightarrow\sf\quad 31 - y - 4y = -9\qquad\qquad\qquad\qquad\sf\Bigg\lgroup From\;eq_{n}\;(i)\Bigg\rgroup$

$\dashrightarrow\sf\quad 31 - 5y = -9$

$\dashrightarrow\sf\quad 31 + 9 = 5y$

$\dashrightarrow\sf\quad 40 = 5y$

$\dashrightarrow\sf\quad y = \cancel\dfrac{40}{5}$

$\dashrightarrow\quad\underline{\boxed{\pmb{\sf{y = 8}}}}$

$\;\:\;\underline{\bf{\dag} \:\;\sf{Now, Using\;eq_{n}\:(i)\; :}}$

$\dashrightarrow\sf\quad x + y = 31$

$\dashrightarrow\sf\quad x = 31 - y$

$\dashrightarrow\sf\quad x = 31 - 8$

$\dashrightarrow\quad\underline{\boxed{\pmb{\sf{x = 23}}}}$

$\therefore{\underline{\textsf{Hence, present age of Manisha and Savita is \textbf{8 years} and \textbf{23 years}.}}}$