Question

The age of Ram and shyam are in the ration 3:4 . Five years ago their ages were in the ration 2:3. Find their present ages​

Answer 1

Answer:

• Present age of Ram is 15 years
• Present age of Shyam is 20 years.

Step-by-step explanation:

Solution:-

Let the ratio of their age be 3x & 4x

According to the Given Condition

Five years ago the ratio of their age 2:3

Therefore,

→ Ram's age = 3x -5 ------(I)

→ Shyam's age = 4x - 5 -----(ii)

Now , Multiplying by 3 in Equation (I) & by 2 in (ii) we get

→ (3x-5)× 3 = (4x-5) × 2

→ 9x - 15 = 8x -10

→ 9x -8x = -10 +15

→ x = 5

Therefore,

Present age of Ram = 3x = 3×5 = 15 years

Present age of Shyam = 4x = 4×5= 20 years

Answer 2

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

$\tt The\: age\: of \:Ram \:and \:shyam\: are\: in\: the \:ration\: 3:4.\\\tt Five\: years\: ago\: their\: ages\: were \:in\: the\: ration \:2:3.\\\tt Find\: their\: present\: ages.$

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

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

• $\sf \bf Present\: age\: of\: Ram\: and\: shyam=3:4$
• $\sf \bf 5 \:years \:ago\: age\: of\: Ram\: and\: shyam=2:3$

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

• $\sf \bf Present \:age \:of \:Ram \:and \:Shyam$

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

${\underbrace {\overbrace {\color {orange} {\sf \bf Present\:age}}}}$

$\tt Let\:the\:age\:of\:Ram\:be=3x$

$\tt Let\:the\:age\:of\:Shyam\:be=4x$

${\underbrace {\overbrace {\color {orange} {\sf \bf 5\:years\:ago}}}}$

$\tt Let\:the\:age\:of\:Ram\:be=3x-5$

$\tt Let\:the\:age\:of\:Shyam\:be=4x-5$

$\sf \underline {According \:to \:the \:question}$

$\sf \bf 3x-5=2\:\:\:and\:\:\:4x-5=3$

$\sf \bf \implies \dfrac{3x-5}{4x-5}=\dfrac{2}{3}$

$\sf \bf \implies 3(3x-5)=2(4x-5)$

$\sf \bf \implies 9x-15=8x-10$

$\sf \bf \implies 9x-8x=15-10$

$\implies {\boxed {\color{green} {\sf \bf x=5}}}$

------------------------------------------------------------

$\tt{\underbrace {\overbrace {\color{purple} {Present\:age\:of \:Ram=3x}}}}$

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

$\implies {\boxed {\boxed {\color {blue} {15\:years}}}}$

$\tt{\underbrace {\overbrace {\color{purple} {Present\:age\:of \:Shyam=4x}}}}$

$\sf \bf \implies 4 \times 5$

$\implies {\boxed {\boxed {\color {blue} {20\:years}}}}$

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

__________________________________________

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

$\tt {Identities}$

$\sf \bf {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}$

$\sf \bf {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}$

$\sf \bf (a+b) (a-b) ={a}^{2}-{b}^{2}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$