Question

The ages of Moroni and Rajini are in the ratio 5:7,4 years from now the ratio of their ages will be 3:4.Find their present ages​

Answer 1

SOLUTION :-

Let,

Present age of Moroni = x

Present age of Rajini = y

After 4 years,

Age of Moroni = x + 4

Age of Rajini = y + 4

According to the first condition,

$\longrightarrow\sf \dfrac{x}{y}=\dfrac{5}{7}\\\\\longrightarrow x =\dfrac{5}{7}y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+4}{y+4}=\dfrac{3}{4} \\\\\longrightarrow 4(x+4)= 3(y+4) \\\\\longrightarrow 4x+16= 3y+12 \\\\\longrightarrow4x-3y = 12-16 \\\\\longrightarrow 4x-3y = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(2)$

Substitute the value of x in equation (2),

$\longrightarrow\sf 4\times \dfrac{5}{7}y -3y= -4 \\\\\longrightarrow \dfrac{20y}{7} - 3y= -4 \\\\\longrightarrow \dfrac{20y-21y}{7} = -4 \\\\\longrightarrow -y = -28\\\\\longrightarrow \bf y = 28$

Substitute the value of y in equation (1),

$\longrightarrow\sf x = \dfrac{5}{7}\times 28\\\\\longrightarrow x =5\times 4\\\\\longrightarrow \bf x = 20$

Present age of Moroni = 20 years

Present age of Rajini = 28 years

Answer 2

Answer:

$\sf Present\:Age \:\:\xrightarrow{After\:4\:Years} \:\:Future\:Age\\{\sf Moroni : Rajini \qquad\qquad\: Moroni: Rajini} \\{ \: \: \: \: \: \: \: \: \: \sf 5 \::\:7 \qquad \qquad \qquad\qquad 3 : 4}$

Let the present age of Moroni be 5x and Rajini be 7x respectively.

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

$:\implies\sf \dfrac{Moroni+4}{Rajini+4}=\dfrac{3}{4}$

$:\implies\sf \dfrac{5x+4}{7x+4}=\dfrac{3}{4}$

$:\implies\sf (5x + 4) \times 4= 3 \times (7x + 4)$

$:\implies\sf 20x + 16 = 21x + 12$

$:\implies\sf 16 - 12 = 21x - 20x$

$:\implies\:\underline{\boxed{\red{\sf x = 4\:years}}}$

_________________....

☯ $\underline{\boldsymbol{Present\: Age\:of\: Moroni\:\&\:Rajini:}}$

$\bullet\:\:\textsf{Moroni = 5x = 5(4) = \textbf{20 years}}\\\bullet\:\:\textsf{Rajini = 7x = 7(4) = \textbf{28 years}}$