Question

The ratio of present ages of Virat and Sachin is 5 : 9. Three years hence ratio of their ages will be 3 : 5. Find Virat's present age?​

Answer 1

Given :-

• Present ages of virat and Sachin are in the ratio 5:6
• After 3 years their ages will be in the ratio 3:5.

To Find :-

• Present Age of Virat.

SᴏʟᴜᴛɪᴏN :-

➟Let percent age of virat be = 5 x

➟Let percent age of Sachin be = 9 x

Aғᴛᴇʀ 3 ʏᴇᴀʀs :

➟ percent age of virat = 5 x + 3

➟ percent age of Sachin = 9 x + 3

A.ᴛ.Q

➟ 5 x + 3 / 9 x + 3 = 3/5

➟ 5 [ 5x + 3 ] = 3 [ 9x + 3 ]

➟ 25 + 15 = 27x + 9

➟25 x - 27 x = 9 - 15

➟- 2x = -6

➟ x = 3

Tʜᴇʀᴇ ғᴏʀᴇ :-

➟ percent age of virat = 5 (3)

➟ 15 years

➟ percent age of Sachin = 9 (3)

➟ 27 years

Answer 2

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt The\: ratio \:of\: present\: ages \:of\: Virat\: and \:Sachin\: is\\\tt 5 : 9.\: Three\: years\: hence\: ratio\: of \:their\: ages \:will\\\tt be\: 3 : 5.\: Find\: Virat's \:present\: age?$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\sf \bf The\: ratio\: of \:present \:ages\: of\: Virat\: and\: Sachin=5:9$
• $\sf \bf The\: ratio\: of \:ages\: of\: Virat \:and\: Sachin\: after\: 3\: years =3:5$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\sf \bf Present\:age\:of\:Virat$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\color {gold} \underline {\sf Let\: the\: present\: age\: of\: Virat\: be\: 5x}}$

${\color {gold} \underline {\sf Let \:the\: present\: age\: of \:Sachin \:be\: 9x}}$

${\color {red}{\underbrace {\bf After \:3 \:years}}}$

${\color {lightgreen} {\sf Age\:of \:Virat=5x+3}}$

${\color {lightgreen} {\sf Age\:of \:Sachin=9x+3}}$

${\underbrace {\overbrace {\color {orange} {\bf According \:to \:the \:question}}}}$

$\sf \bf \implies \dfrac{5x+3}{9x+3}=\dfrac{3}{5}$

$\sf \bf \implies 3\Big(9x+3\Big) = 5\Big(5x+3\Big)$

$\sf \bf \implies 27x+9=25x+15$

$\sf \bf \implies 27x-25x=15-9$

$\sf \bf \implies 2x=6$

$\sf \bf \implies x=\dfrac{6}{2}$

$\implies {\boxed {\boxed {\color {blue} {\sf \bf x=3}}}}$

${\color {indigo} {\sf Virat's \:present \:age =5x}}$

$\sf \bf \implies 5 \times 3$

$\implies {\boxed {\boxed{\boxed{\color {green} {\sf \bf 15\:years}}}}}$

${\color{red} {\underbrace {\underline {\sf \therefore The\:present\:age\:of\: Virat\:is\:15 \:years}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

__________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

${\color {purple} {\sf Sachin's\:present \:age =9x}}$

$\sf \bf \implies 9 \times 3$

$\implies {\boxed {\boxed{\boxed{\color {yellow} {\sf \bf 27\:years}}}}}$

${\color{magenta} {\underline {\sf \therefore The\:present\:age\:of \:Sachin\:is\:27 \:years}}}$