Question

(4) Sum of the present ages of Manish and Savita is 31. Manish's age 3 years ago
was 4 times the age of Savita. Find their present ages.
​

Answer 1

Let the present age of Manish be x years and the present age of Savita be y years.

Sum of their present ages = 31

➨ x + y = 31......{Equation (1)}

3 years ago,

• Manish's age = (x - 3) years.

• Savita's age = (y - 3) years.

☯$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

➨ (x - 3) = 4(y - 3)

➨ x - 3 = 4y - 12

➨ x = 4y - 12 - 3

➨ x = 4y - 9......{Equation (2)}

Putting equation (2) in equation (1) we get :

➨ x + y = 31

➨ 4y - 9 + y = 31

➨ 4y + y = 31 + 9

➨ 5y = 40

➨ y = 40/5

➨ y = 8 years

Putting the value of y in equation (1) :-

➨ x + y = 31

➨ x + 8 = 31

➨ x = 31 - 8

➨ x = 23 years

$\rule{130}1$

☯ $\underline{\boldsymbol{Present\: Age\:of\: Savita\:\&\:Manish:}}$

$\begin{lgathered}\bullet\:\:\textsf{Savita = y = \textbf{8 years}}\\\bullet\:\:\textsf{Manish = x = \textbf{23 years}}\end{lgathered}$

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow Sum\:of \:the\: present\: ages\: of\: Manish \:and\: Savita\: is \:31$

$\sf\dashrightarrow manish\:age\:3\:years\:ago\:was\:4\:times\:the\:age\:of\:savita$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THERE\:BOTH'S\:PRESENT\:AGES.$

ACCORDING TO THE QUESTION,

$\sf\dashrightarrow taking\:'x'\:years\:age\:of\:manish\:and\:'y'\:years\:as\:savita.$

$\sf\therefore sum\:of\:there\:both\:age=32\:years$

$\sf\large\therefore x+y=31........eq^1$

$\sf\therefore manish\:age\:3\:years\:ago\:was\:4\:times\:the\:age\:of\:savita$

THEN,THE AGE OF BOTH 3 YEARS AGO WILL BE,

$\sf\therefore manish=(x-3)$

$\sf\dashrightarrow savita=(y-3)$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore (x - 3) = 4 \times (y - 3)$

$\sf\implies (x - 3) = 4y - 12$

$\sf\implies x=4y-12+3$

$\sf\implies x=4y-9........eq^2$

$\sf{\boxed{\sf{ x=4y-9}}}$

SUBSTITUTING THE VALUE OF (EQ²)'X' IN EQUATION 1

$\sf\therefore x + y = 31$

$\sf\implies (4y - 9) + y = 31$

$\sf\implies 4y+y-9=31$

$\sf\implies 4y + y = 31 + 9$

$\sf\implies 5y = 40$

$\sf\implies y= \dfrac{40}{5}$

$\sf\implies y= \cancel \dfrac{40}{5}$

$\sf\implies y=8$

$\large{\boxed{\bf{ y(SAVITA)=8\:years}}}$

NOW, FINDING THE VALUE(AGE) OF'X'(MANISH),

SUBSTITUTING THE VALUE OF Y IN EQUATION 1

$\sf\implies x + y = 31$

$\sf\implies x + 8 = 31$

$\sf\implies x = 31 - 8$

$\sf\implies X=23$

$\large{\boxed{\bf{ X(MANISH)=23\:years}}}$

$\sf\large\underline\bold{THE\: PRESENT\:AGE\:OF\:MANISH\:IS\:23\:YEARS,}$

$\sf\large\underline\bold{THE\: PRESENT\:AGE\:OF\:SAVITA\:IS\:8\:YEARS.}$

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