Question

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\purple{Question:}}}}}}}\end{gathered}$
Hitesh is 40 years old and Rohit is 60 years old. How many years ago was the ratio of their ages 3 : 5?
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Answer 1

$\large{\underline{\underline{\pmb{\frak{ Given :- }}}}}$

• Hitesh is 40 years old
• Rohit is 60 years old

$\large{\underline{\underline{\pmb{\frak{ To\;find :- }}}}}$

• How many years ago was the ratio of their ages 3 : 5 ?

$\large{\underline{\underline{\pmb{\frak{ solution :- }}}}}$

~Here, we're given that Hitesh is 40 years old and Rohit is 60 years old and we need to find how many years ago was the ratio of their ages 3 : 5. Firstly, we'll assume the years be 'x' and then we'll form an equation according to the question. After solving that equation we'll get the required answer.

___________

★ Let the number of years be ' x '

According to the question :-

$\sf \dashrightarrow \dfrac{40-x}{60-x} = \dfrac{3}{5}$

$\sf \maltese \;\;\; Cross \; multiply$

$\sf \dashrightarrow 5\{40-x\} = 3\{60-x\}$

$\sf \dashrightarrow 200-5x = 180-3x$

$\sf \dashrightarrow 5x-3x =200 -180$

$\sf \dashrightarrow 2x = 20$

$\sf \dashrightarrow x = \dfrac{20}{2}$

$\bigstar \: \underline{\boxed{\bf{x = 10}}}$

Hence,

• 10 years ago ratio of their ages was 3 : 5.

Answer 2

Answer:

${ \underline{ \large{ \pmb{ \sf{Given... }}}}}$

• Hitesh age = 40years
• Rohit age = 60years

$\: { \underline{ \large{ \pmb{ \sf{Find...}}}}}$

• How many years ago was the ratio of their ages 3 : 5?

${ \underline{ \large{ \pmb{ \sf{Solution... }}}}}$

• In question they mentioned that how many years ago so, we have to do minus to the following ages

• Let us assume that x years ago their ages ratio is 3 : 5

• Hitesh age = 40 - x
• Rohit age = 60 - x

According to question,

$: { \implies{ \sf{ \frac{40 - x}{60 - x} = \frac{3}{5} }}} \\ \\ { \sf{let \: us \: do \: cross \: multiplication}} \\ \\ : { \implies{ \sf{5(40 - x) = 3(60 - x)}}} \\ \\ : { \implies{ \sf{200 - 5x = 180 - 3x}}} \\ \\ : { \implies{ \sf{200 - 180 = - 3x + 5x}}} \\ \\ : { \implies{ \sf{20 = 2x}}} \\ \\ : { \implies{ \sf{x = \frac{20}{2} }}} \\ \\ : { \implies{ \sf{ \bold{x = 10}}}}$

$\therefore{ \sf{ \underline{10 \: years \: ago \: their \: ages \: ratio \: is \: 3:5}}}$

${ \underline{ \large{ \pmb{ \sf{Verification...}}}}}$

$\to{ \sf{40 - x :60 - x = 3 : 5 }} \\ \\ \to{ \sf{40 - 10 :60 - 10 = 3 :5 }} \\ \\ \to \sf{30 :50 = 3 :5 } \\ \\ \to \sf{3 :5 = 3 :5 } \: \: \\ \\ { \therefore{ \bold{ {Hence \: Proved}}}}$