Question

Raju is 19 years younger than his cousin after 5 years their ages will be in the ratio of 2:3 find their present age

Answer 1

$\LARGE\underline\mathfrak{AnSwEr:}$

$\star$ $\normalsize\sf\green{Present \: age \: of \: Raju \: is \: 33 \: yrs.}$

$\star$ $\normalsize\sf\blue{Present \: age \: of \: Raju's \: cousin \: is \: 52 \: yrs}$

$\LARGE\underline\mathfrak{Step \: by \: step \: explanation:}$

➠$\normalsize\sf{ Let \: the \: age \: of \: Raju \: cousin's \: be \: \red{ M \: yrs} }$

$\scriptsize\sf{\: \: \: \: \: \: \: (Also, \: Raju \: is \: \pink{19 \: years} \: younger \: than \: his \: cousin \: so,)}$

➠$\normalsize\sf{ Raju's \: age \: = \red{ (\: x\: - \: 19) \: years} }$

$\normalsize\underline\textsf{Now; \: according \: to \: question }$

$\scriptsize\sf{ \: \: \: \: \: \: \: \: \: \: \:(After \: 5 \: years \: ratio \: of \: their \: ages \: is \: \pink{2:3},let's \: solve)}$

➠$\Large\sf\frac{(x \: - \: 19) \: + \: 5}{x \: + \: 5} \: = \: \frac{2}{3}$

➠$\Large\sf\frac{ x \: - \: 14}{x \: + \: 5} \: = \: \frac{2}{3}$

$\scriptsize\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:( By \: \pink{cross \: multiplication}) }$

➠$\small\sf\ 3( x \: - \: 14) \: = \: 2( x \: + \: 5)$

➠$\small\sf\ 3x \: - \: 42 \: = \: 2x \: + \: 10$

➠$\small\sf\ 3x \: - \: 2x \: = \: 10 \: + \: 42$

➠$\small\sf\ x \: = \: \green{52}$

➠${\boxed{\sf \orange{Age \: of \: Raju's \: cousin \: = \: 52 \: yrs.}}}$

$\scriptsize\sf{ \: \: \: \: \: \: \: \: \: \: \: \: (Now, \: let's \: find \: \pink{age \: of \: Raju:})}$

➠$\small\sf\ Age \: of \: Raju \: = \: (\: x \: - \: 19)$

➠$\small\sf\ Age \: of \: Raju \: = \: (\: 52 \: - \: 19) \: = \: 33$

➠${\boxed{\sf \orange{Age \: of \: Raju \: = \: 33yrs.}}}$

Answer 2

$\Huge\mathfrak\red{Question:}$

ʀᴀᴊᴜ ɪs 19 ʏᴇᴀʀs ʏᴏᴜɴɢᴇʀ ᴛʜᴀɴ ʜɪs ᴄᴏᴜsɪɴ. ᴀғᴛᴇʀ 5 ʏᴇᴀʀs ᴛʜᴇɪʀ ᴀɢᴇs ᴡɪʟʟ ʙᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ 2:3 .ғɪɴᴅ ᴛʜᴇɪʀ ᴘʀᴇsᴇɴᴛ ᴀɢᴇ.

$\Huge\mathfrak\green{Answer:}$

${\boxed{\orange{\sf{Raju's \: present \: age = 33}}}}$

${\boxed{\orange{\sf{His \: cousin's \: present \: age = 52}}}}$

$\large\mathrm\blue{Step-by-step \: explanation: }$

ʟᴇᴛ ʀᴀᴊᴜ's ᴄᴏᴜsɪɴ's ᴘʀᴇsᴇɴᴛ ᴀɢᴇ ʙᴇ = x

ʟᴇᴛ ʀᴀᴊᴜ's ᴘʀᴇsᴇɴᴛ ᴀɢᴇ ʙᴇ = x-19

ᴛʜᴇɪʀ ᴀɢᴇs ᴀғᴛᴇʀ ғɪᴠᴇ ʏᴇᴀʀs ;

ʀᴀᴊᴜ = x -19 + 5 = x - 14

ᴄᴏᴜsɪɴ = x +5

ʀᴀᴛɪᴏ ᴏғ ᴛʜᴇɪʀ ᴀɢᴇs ᴀғᴛᴇʀ ғɪᴠᴇ ʏᴇᴀʀs = 2:3

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ϙᴜᴇsᴛɪᴏɴ :-

ʀᴀᴊᴜ's ᴀɢᴇ : ʜɪs ᴄᴏᴜsɪɴ's ᴀɢᴇ

$\tt{x - 14 : \: x + 5 = 2 : 3}$

$\tt{ \frac{x - 14}{x + 5} = \frac{2}{3} }$

$\tt\small{ \: By \: cross \: \: multiplication : }$

$\tt{3(x - 14) = 2(x + 5)}$

$\tt{3x - 42 = 2x + 10}$

$\tt{ 3x - 2x = 10 + 42 }$

$\tt \huge{x = 52}$

$\bf\pink{Hence,}$

$\small\bf\pink{Raju's \: cousin's \: present \: age = x = 52}$

$\small\bf\pink{Raju's \: present \: age = x-19= 52-14= 33}$

$\huge\mathrm\red{Verification:}$

ʀᴀᴊᴜ's ᴘʀᴇsᴇɴᴛ ᴀɢᴇ = 33

ʜɪs ᴄᴏᴜsɪɴ's ᴘʀᴇsᴇɴᴛ ᴀɢᴇ = 52

ᴛʜᴇɪʀ ᴀɢᴇs ᴀғᴛᴇʀ ғɪᴠᴇ ʏᴇᴀʀs =

ʀᴀᴊᴜ's = 33+5 = 38

ʜɪs ᴄᴏᴜsɪɴ's = 52+5 = 57

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ϙᴜᴇsᴛɪᴏɴ ; ʀᴀᴛɪᴏ = 2:3

sᴏ, ᴄʜᴇᴄᴋɪɴɢ =

LHS = 2:3

RHS =

$\tt{ 38 : 57 }$

$\tt{ \frac{38 \div 19 }{ 57 \div 19 } = \frac{2}{3} }$

2:3 = 2:3

ʟʜs = ʀʜs

ʜᴇɴᴄᴇ, ᴠᴇʀɪғɪᴇᴅ :)