Question

age of ramya and the double the age of sofi added together gives 28 .three fourth of ramya age added to one fourth of sofi's age gives 11 .find the age of ramya and age of sofi​

Answer 1

Given :

• age of ramya and double the age of sofi = 28
• three fourth of age of ramya and one fourth of age of sofi = 11

.

To find :

• Age of Ramya and Sofi

.

Solution :

.

Let the age of Ramya be 'x' and the age of Sofi be 'y'

__________

Age of Ramya and double the age of Sofi = 28

$\implies{x+2y=28}$ ---> eq 1

.

Three fourth age of Ramya and one fourth age of Sofi = 11

$\implies{{\frac{3}{4}}x+{\frac{1}{4}}y=11}$ ---> eq 2

Multiply eq 2 by 8 on both sides ..

$\implies{6x+2y=88}$ ( On multiplying by 8 ) ---> eq 3

__________

Subtract eq 1 from eq 3

$\qquad\sf 6x + \cancel{2y} = 88\\\qquad\sf \:x\; + \cancel{2y} = \:28 \\\sf\footnotesize\underline{ \;\;(-)\quad(-)\qquad\;\;(-)\qquad} \\\underline{\sf \qquad \qquad \quad 5x = 60 \: \: \: }$

$\implies {x = {\dfrac{{\cancel{60}}_{12}}{{\cancel{5}}}}}$

$\implies{\boxed{x=12}}$

___________

Substitute x in eq 1

$\implies{x+2y=28}$

$\implies{12+2y=28}$

$\implies{2y=28-12}$

$\implies{2y=16}$

$\implies{y={\dfrac{{\cancel{16}}_{8}}{2}}}$

$\implies{\boxed{y=8}}$

_________________

Age of Ramya = 12 years (x)

Age of Sofi = 8 years (y)

Answer 2

Age of Ramya = x = 12 years.

Age of Sofi = y = 8 years.