Question

sharad is 60 years old and santosh is 80 years old. how many years ago was the ratio of their ages 4 : 6?

Answer 1

$\textbf{Answer:}$

To calculate how many years ago the ratio of their ages were 4:6

We have to assume the years = x

$age \: of \: sharad = 60 -x \\ \\ age \: of \: santosh = 80 - x$
X years ago the ratio of their ages were 4:6

$\frac{(60 - x)}{(80 - x)} = \frac{4}{6} \\ \\ = > 6(60 - x) = 4(80 - x) \\ \\ = > 360 - 6x = 320 - 4x \\ \\ x = 20$

Thus the ratio of their ages were 4:6 20 years ago.

$\textbf{Hope it helps you!}$

Answer 2

$\: \mathbf{ Let \: the \: required \: time \: period \: is \: \: x \: years}$


According to the question,


$\text{Age \: of \: Sharad \: before \: \: x years : \: Age \: of \: Santosh \: before \: \: x \: years = 4 : 6 }$

$=> ( 60 - x ) : ( 80 - x ) = 2 : 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( 4: 6 = 2: 3)$




By Cross Multiply,


=> 3( 60 - x ) = 2( 80 - x )

=> 180 - 3x = 160 - 2x

=> 180 - 160 = 3x - 2x

=> 20 = x





$\mathbb{Hence, \: this \: incident \: was \: happened \: before \: \: 20 \: years}$