Question

Rakesh age is 10% that of Mohan's age and 20% that of shyam's age. what percent of Mohan's age is shyam's age?
please give full explanation​

Answer 1

$\mathsf{let\:Mohan's\:age\:= x}$

$\mathsf{and\:Shyam's\:age\:= y}$

$\fbox{\mathsf{Given\:that\: :}}$

$\mathsf{Rakesh's\:age\: = 10\% \:of\:Mohan's\:age}$

$\mathsf{\implies\: Rakesh's\:age\: = 10\%\:of\:x}$

$\mathsf{\implies\: Rakesh's\:age\: = \frac{10}{100} × \:x}$

$\mathsf{\implies\: Rakesh's\:age\: = \frac{x}{10}\rightarrow\:(1)}$

$\mathsf{Rakesh's\:age\: = 20\%\:of\:Shyam's\:age}$

$\mathsf{\implies\: Rakesh's\:age\: = 20\%\:of\:y}$

$\mathsf{\implies\: Rakesh's\:age\: = \frac{20}{100} × \:y}$

$\mathsf{\implies\: Rakesh's\:age\: = \frac{y}{5}\rightarrow\:(2)}$

$\mathsf{from\:(1) \:and\:(2) }$

$\mathsf{\implies\: \frac{x}{10} = \frac{y}{5}}$

$\mathsf{\implies\: 5x= 10y}$

$\mathsf{\implies\: x = 2y}$

$\mathsf{So, \:Mohan's\: age\: = x = 2y}$

$\mathsf{and, \:Shyam's\: age\: = y}$

$\fbox{\mathsf{Converting \:them\:to\:percentage}}$

$\mathsf{\implies\: \frac{2y}{y} × 100 = \fbox{200\%} }$

Therefore, Mohan's age is 200% to that of Shyam's age