Question

The sum of ages of Priyanka and Deepika is 32 year. Priyanka is eldes to Deepika by 6 years. Then find ther todays ages​

Answer 1

Solution :-

According to the question,

The sum of ages of priyanka and Deepika is 32 year

Let the ages of priyanka and deepika be x and y

Therefore,

x + y = 32 ...eq( 1 )

Now,

Priyanka is eldest to deepika by 6 years

x - y = 6. ...eq( 2 )

Take eq( 1 )

x + y = 36. ...eq( 1 )

x = 32 - y. ... eq( 3 )

Subsitute eq( 3) in eq( 2 )

x - y = 6

( 32 - y) - y = 6. [ From 3 ]

32 - y - y = 6

32 - 2y = 6

-2y = 6 - 32

-2y = -26

y = -26/-2

y = 13

Subsitute the value of y in eq( 1 )

x + y = 32

x + 13 = 32

x = 32 - 13

x = 19

Hence, The age of priyanka and deepika is 19 years and 13 years $.$

Answer 2

$\maltese\LARGE\textsf\textcolor{aqua}{\underline{ SoLuTioN :-}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{Let the age of Priyanka be " x "}$

$\qquad\tt{:}\longrightarrow\large\textsf{And let the age of Deepika be " y "}$

$\large\textsf{ }$

↦ According to the first condition given above :-

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\color{purple}{x + y = 32 ------( i )}}$

$\large\textsf{ }$

↦ According to the second condition given above :-

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\color{purple}{x - y = 6 ------( ii )}}$

$\large\textsf{ }$

↦ Adding ( i ) & ( ii ) :-

$\large\textsf{ }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: x \: \: + \: \: \cancel y \: \: = \: \: 32 \\ \sf ( \: + \: ) \: \: \: \: \: \: \: x \: \: - \: \: \cancel y \: \: = \: \: 6 \: \: \: \\ \sf ------------\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf2x \: \: \: \: \: = \: \: \: \: 38 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: x \: \: \: \: = \: \: \: \: \xcancel \cfrac{38}{2} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \boxed{ \color{red} \sf x \: = \: 19}$

$\large\textsf{ }$

↦ Substituting the value of " x " in (i)

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{19 + y = 32}$

$\qquad\tt{:}\longrightarrow\large\textsf{y = 32 - 19}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\color{red}{y = 13}}$

$\large\textsf{ }$

$\boxed{\begin{array}{c}\\\leadsto\large\textsf\textcolor{orange}{ Priyanka's age = 19 years}\\\\\leadsto\large\textsf\textcolor{orange}{Deepika's age = 13 years}\\\end{array}}$