Question

TodAy Question
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present ages of anu and from now the ratio of their age Raj are in the ratio 4:5.eight year from now the ratio of their ages will be 5:6.find their present age ?​

Answer 1

Answer:

${\underline{\bold\green{Present\:age\:of\:Anu = 32\: years}}}$

${\underline{\bold\purple{Present\:age\:of\:Raj = 40\: years}}}$

$\frak\red{Given:-}\begin{cases}\sf\green{Present\: ratio\:of\: ages = 4 : 5}\\\sf\purple{After\:8\:years\:ratio\:will\:be = 5 : 6}\\\sf\blue{Present\:ages\:of\:both = ?}\end{cases}$

Let present age of Anu and Raj be 4x and 5x respectively.

$\therefore$ After 8 years, age of Anu =(4x + 8) years.

$\therefore$ After 8 years, age of Raj =(5x + 8) years.

$\sf{A/Q,}$

$\implies\sf (4x + 8) : (5x + 8) = 5 : 6 \\\\\implies\sf \dfrac{4x + 8}{5x + 8} =\dfrac{5}{6} \\\\\implies\sf 6(4x + 8) = 5(5x + 8) \\\\\implies\sf 24x + 48 = 25x + 40 \\\\\implies\sf 25x - 24x = 48 - 40 \\\\\implies{\boxed{\sf\blue{x = 8}}}$

$\rule{200}{1}$

Ages of Anu and Raj :-

$\sf Present\:age \:of\:Anu = 4x = 4(8) = 32\:years$

$\sf Present\:age\: of \:Raj = 5x = 5(8) = 40\:years$

${\underline{\boxed{\therefore{\sf\green{Present \: age \: of \: Anu = 32\:years}}}}}$

${\underline{\boxed{\therefore{\sf\blue{Present\:age\:of\:Raj = 40\:years}}}}}$

Answer 2

$\huge{\overline{\underline{\bf{Answer}}}}$

➠$\small\underline\textsf{The present age of Anu =\red{32years}}$

➠$\small\underline\textsf{The present age of Raj =\red{40years}}$

$\large\underline\frak{Suppose}$

$\star\small\textsf{ The present age of Anu be =\red{4x years }}$

$\star\small\textsf{ The present age of Raj be =\red{5x years}}$

$\huge\underline\textsf{Explantion:- }$

$\small\star\texttt{ After eight years.Anu's age = \blue{(4x+8)years.}}$

$\small\star\texttt{ After eight years.Raj's age = \blue{(5x+8)years.}}$

$\large\underline\frak{ therefore, }$

$\small\sf{ the\: ratio \:of \:their \:ages \:after\: eight\: years =\boxed{\tt{ \dfrac{4x + 8} {5x + 8} }}}$

➠$\textsf {this \: is \: given \: to \: be \: 5:6}$

$\large\star\underline\textsf{Cross Multiplication }$

$\implies\sf6(4x + 8) = 5(5x + 8)$

$\implies\sf24x + 48 = 25x + 40$

$\implies\sf24x + 48 - 40 = 25x$

$\implies\sf24x8 = 25x$

$\implies\sf8 = 25x - 24x$

$\implies\sf8 = x$

$\implies\sf x = 8$

$\large\underline\frak{ therefore, }$

$\star\sf anu \: present \: age \: = 4x \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 \times 8 \\\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 32 \: years$

$\star\tt raj \: present \: age = 5x \\ \tt\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5 \times 8 \\\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 40 \: years$

➠$\small\underline\textsf{The present age of Anu =\red{32years}}$

➠$\small\underline\textsf{The present age of Raj =\red{40years}}$