Question

the ages hari and harry are in the ratio 5:7 Four years from now the ratio of their ages will be 3:4 Find their presentage ages​

Answer 1

Answer:

Given :-

• The ages of Hari and Harry are in the ratio of 5 : 7.
• Four years from now the ratio of their ages will be 3 : 4.

To Find :-

• What is their present ages.

Solution :-

Let,

$\leadsto \bf{Present\: age\: of\: Hari =\: 5x\: years}$

$\leadsto \bf{Present\: age\: of\: Harry =\: 7x\: years}$

❒ Four years from now :

$\mapsto \sf Age\: of\: Hari =\: (5x + 4)\: years$

$\mapsto \sf Age\: of\: Harry =\: (7x + 4)\: years$

According to the question,

$\implies \bf (5x + 4) : (7x + 4) =\: 3 : 4$

$\implies \sf \dfrac{5x + 4}{7x + 4} =\: \dfrac{3}{4}$

By doing cross multiplication we get,

$\implies \sf 3(7x + 4) =\: 4(5x + 4)$

$\implies \sf 21x + 12 =\: 20x + 16$

$\implies \sf 21x - 20x =\: 16 - 12$

$\implies \sf\bold{\purple{x =\: 4\: years}}$

Hence, the required ages of Hari and Harry are :

➲ Present Age of Hari :

$\longrightarrow \sf Present\: Age_{(Hari)} =\: 5x\: years$

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

$\implies \sf\bold{\red{Present\: Age_{(Hari)} =\: 20\: years}}$

➲ Present Age of Harry :

$\longrightarrow \sf Present\: Age_{(Harry)} =\: 7x\: years$

$\longrightarrow \sf Present\: Age_{(Harry)} =\: 7 \times 4\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Harry)} =\: 28\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Hari\: and\: Harry\: is\: 20\: years\: and\: 28\: years\: respectively\: .}}}}$

Answer 2

$\large \underline \bold \green { Given:- \: }$

$\bold{\bold\rightarrow\:The \: \: ages \: \: Hari \: \: and \: \: Harry \: \: are \: \: in \: \: the \: \: ratio \: 5:7 \: }$

$\bold{\bold\rightarrow\:Four \: \: years \: \: from \: \: now \: \: the \: \: ratio \: of \: their \: }$

$\bold{ages \: will \: be \: 3:4}$

$\large \underline \bold \blue{ to \: find \: :- \: }$

$\bold{ \bold\rightarrow\: what \: is \: their \: percentage}$

$\large \underline \bold \blue{ Solution \: :- \: }$

$\bold { Let \: Hari's \: age = 5 \: x \: years} \\ \\ \: </p><p></p><p> \bold {and \: harry 's\: \: age = 7 \: x \: years }$

$\bold \red {after \: four \: years, \: }$

$\bold{Hari 's \: \: age \: = (5x + 4) \: years} \\ \\</p><p>\bold{and \:Harry's \: age \: = (7x + 4) \: years} \\ \\ </p><p>$

$\bold \pink{given \: \: that, \: }$

$\bold{The \: \: ratio \: of \: Hari's \: age \: and \: Harry \:} \\ \:$

$\bold{age \: after \: 4 \: years \: from \: now = 3:4 \: } \:$

$\bold { \bold\rightarrow \frac{ \:Hari's \: age \: after \: 4 \: years \: }{ \:Harry's \: age \: after \: 4 \: years \: } = \frac{3}{4} } \\ \:$

$\bold { \bold\rightarrow \frac{ 5x + 4 \: }{ 7x + 4} = \frac{3}{4} } \\ \:$

$\bold { \bold\rightarrow 4 (5x+4)=3 (7x+4) \: \: } \\ \:$

$\bold { \bold\rightarrow \: 20x + 16 = 21x + 12 \: \: } \\ \:$

$\bold { \bold\rightarrow 16-12 = 21x- 20x \: \: } \\ \:$

$\bold { \bold\rightarrow \: 4 = x } \\ \:$

$\bold \green { \bold\rightarrow \: x \: = 4} \\ \:$

$\bold \pink{Therefore,}$

$\bold {Present \: age \: of \: Hari = 5x = 5 x \: 4 \: \: \: }$

$\bold \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20years} \:$

$\bold {Present \: age \: of \: Harry= 7x = 7 \: x \: 4 \: }$

$\bold \purple{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 28 \: years} \:$