Question

Ratio of ages of ram and shyam is 3.4 sum of their ages after 5 yearswe'll be 45 years find their Present age​

Answer 1

Answer:

Given :-

• The ratio of ages of Ram and Sam is 3 : 4.
• Sum of their ages after 5 years will be 45 years.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: age\: of\: Ram =\: 3x\: years$

$\mapsto \bf Present\: age\: of\: Shyam =\: 4x\: years$

➦ After 5 years :

$\leadsto \sf Age\: of\: Ram =\: (3x + 5)\: years$

$\leadsto \sf Age\: of\: Shyam =\: (4x + 5)\: years$

According to the question,

$\implies \sf (3x + 5) + (4x + 5) =\: 45$

$\implies \sf 7x + 10 =\: 45$

$\implies \sf 7x =\: 45 - 10$

$\implies \sf 7x =\: 35$

$\implies \sf x =\: \dfrac{\cancel{35}}{\cancel{7}}$

$\implies \sf\bold{\purple{x =\: 5}}$

Hence, the required ages of Ram and Shyam are :

❒ Present Age Of Ram :

$\longrightarrow \sf Present\: Age_{(Ram)} =\: 3x\: years$

$\longrightarrow \sf Present\: Age_{(Ram)} =\: 3 \times 5\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Ram)} =\: 15\: years}}$

❒ Present Age Of Shyam :

$\longrightarrow \sf Present\: Age_{(Shyam)} =\: 4x\: years$

$\longrightarrow \sf Present\: Age_{(Shyam)} =\: 4 \times 5\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Shyam)} =\: 20\: years}}$

${\footnotesize{\bold{\underline{\therefore\: The\: present\: age\: of\: Ram\: and\: Shyam\: is\: 15\: years\: and\: 20\: years\: respectively\: .}}}}$

Answer 2

$\large \tt {Skilfully\: Questioned✓}$

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$\huge \rm {Answer:-}$

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$\small \bf \blue{According\: to\: the\: Question:-}$

$\dashrightarrow \tt {Ratio\: of\:ages\: of}$ $\tt{ram\: and\: shyam\: is\: 3:4}$

$\dashrightarrow \tt {Sum\: of\:their\: ages\: after}$ $\tt {5\: years\: will\: be\: 45}$

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$\small \bf \pink {To\: find:-}$

$\dashrightarrow \tt {Present\: age\: of\: Ram=?}$

$\dashrightarrow \tt {Present\: age\: of\: shyam=?}$

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$\small \bf \purple{Consideration:-}$

$\dashrightarrow {Let\: Ram's\: age\: be\: 3x }$

$\dashrightarrow {Let\: Shyams\: age\: be\: 4x }$

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$\small \bf \red{After\: 5\: years,}$

$\dashrightarrow { Ram's\: age=3x+5 }$

$\dashrightarrow { Shyam's\: age=4x+5 }$

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★According to the condition given in the question,

$\small \dashrightarrow \tt {Sum\: of\:their\: ages\: after}$ $\tt{5\: years\: will\: be\: 45}$

$\colon \to {3x+5+4x+5=45}$

$\colon \to {7x+10=45}$

$\colon \to {7x=45-10}$

$\colon \to {7x=35}$

$\large \colon \to {x=\frac{35}{7}}$

$\large \colon \to {x=\frac{\cancel{35}^{5}}{\cancel{7}_{1}}}$

$\implies \orange {\fbox{X=5}}$

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★As we found the value of 'x', we can find ram and shaym's present ages .

$\dashrightarrow { Ram's\: present\:age=3x }$

$\dashrightarrow { Ram's\: Present\:age=3(5)}$

$\small \implies \green {\fbox{Ram's\: Present\:age=15years}}$

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$\dashrightarrow { Shyam's\: present\:age=4x }$

$\dashrightarrow { Shyam's\: present\:age=4(5) }$

$\small \implies \green {\fbox{Shyam's\: Present\:age=20years}}$

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★Henceforth,

$\implies \tt{Their\: present\: ages\: are\:}$ $\tt{ 15\:years\: and\: 20\: years}$ $\tt {respectively.}$