the present ages of ajay and vijay are in ratio 4:5. Four years from now their ages will be in ratio 5:6. Find their present age. No spam About the author Josie
❍ The Given ratio of present ages of Ajay and Vijay is 4: 5. So, Let’s say the present ages of Ajay and Vijay are 4x and 5x respectively. ☆ Four years from now their ages — Ajay’s age after four years = (4x + 4) Vijay’s age after four years = (5x + 4) ⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀ ⠀⠀⠀⠀⠀ [tex]\underline{\bigstar\:\boldsymbol{According\; to \;the \;given \;Question :}}[/tex] ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ Four years from now their ages (Ajay’s age and Vijay’s age) will be in the ratio of 5: 6. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ Therefore, ⠀ [tex]:\implies\sf \bigg(\dfrac{4x + 4}{5x + 4} \bigg) = \bigg(\dfrac{5}{6}\bigg) \\\\\\:\implies\sf 6(4x + 4) = 5(5x + 4) \\\\\\:\implies\sf 24x + 24 = 25x + 20\\\\\\:\implies\sf 24x – 25x = 20 – 24 \\\\\\:\implies\sf -x = -4\\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{x = 4}}}}}\;\bigstar[/tex] ⠀ Hence, ⠀ Ajay’s present age = 4x = 4(4) = 16 years Vijay’s present age = 5x = 5(4) = 20 years ⠀ [tex]\therefore{\underline{\sf{Hence, their\: present\;ages\:are\;\bf{16\; years\;\&\;20\:years }.}}}[/tex] [tex]\rule{250px}{.3ex}[/tex] ⠀ V E R I F I C A T I O N : ⠀ It is given as, Four years from now their ages (Ajay’s age and Vijay’s age) will be in the ratio of 5: 6. So, let’s verify their ages : ⠀ [tex]\dashrightarrow\sf \dfrac{4x + 4}{5x + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{4(4) + 4}{5(4) + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{16 + 4}{20 + 4} = \dfrac{5}{6}\\\\\\\dashrightarrow\sf \cancel\dfrac{20}{24} = \dfrac{5}{6} \\\\\\\dashrightarrow\underline{\boxed{\frak{\dfrac{5}{6} = \dfrac{5}{6}}}}[/tex] ⠀ [tex]\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}[/tex] ⠀⠀⠀⠀⠀⠀⠀ Reply
Given : The present ages of ajay and vijay are in ratio 4:5 & four years from now their ages will be in ratio 5:6. Exigency to find : The Present age of Ajay and Vijay . ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ ❒ Let’s consider the Present ages of Ajay and Vijay be 4x and 5x yrs , respectively . ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:According \: to \: \: the \: Question \: \::}}\\[/tex] ⠀⠀⠀⠀⠀━━━ Four years from now the ages of Ajay and Vijay will be in ratio 5:6. [tex]\qquad \longmapsto \sf \dfrac{ Present \:Age\:of\:Ajay\: + 4 }{ Present \:Age\:of\:Vijay\: + 4 } = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \sf \dfrac{ 4x\: + 4 }{ 5x\: + 4 } = \dfrac{5}{6} \\\\[/tex] ⠀⠀⠀⠀⠀By Cross Multiplication : [tex]\qquad \longmapsto \sf \dfrac{ 4x\: + 4 }{ 5x\: + 4 } = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \sf 6(4x\: + 4) = 5( 5x\: + 4) \\\\[/tex] [tex]\qquad \longmapsto \sf 24x\: + 24 = 5(5x\: + 4) \\\\[/tex] [tex]\qquad \longmapsto \sf 24x\: + 24 = 25x\: + 20 \\\\[/tex] [tex]\qquad \longmapsto \sf 24x\: = 25x\: + 20 – 24 \\\\[/tex] [tex]\qquad \longmapsto \sf 24x\: = 25x\: – 4 \\\\[/tex] [tex]\qquad \longmapsto \sf 24x\: – 25x = \: – 4 \\\\[/tex] [tex]\qquad \longmapsto \sf -x\: = \: – 4 \\\\[/tex] [tex]\qquad \longmapsto \sf \cancel{-} x\: = \: \cancel{-} 4 \\\\[/tex] [ “-ve” sign will be eliminated from both side] [tex]\qquad \longmapsto \frak{\underline{\purple{\:x = 4\:yrs }} }\:\:\:\bigstar \\[/tex] Therefore, Present age of Ajay is 4x = 4(4) = 16 yrs . Present age of Vijay is 5x = 5(4) = 20 yrs . Therefore, ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \sf {\:Present \:age\:of\:Ajay \:and\:Vijay \:is}\:\bf{16\:yrs \:and\:20\:yrs}\:\:\sf{,respectively}}}\\[/tex] [tex]\rule200{1.5}[/tex] [tex]\large {\boxed{\sf{\mid{\overline {\underline {\star \: Verification \::}}}\mid}}}\\\\[/tex] Given that : ⠀⠀⠀⠀⠀━━━ Four years from now the ages of Ajay and Vijay will be in ratio 5:6. The Present ages of Ajay and Vijay are 16 yrs & 20 yrs ,respectively. [tex]\qquad \longmapsto \sf \dfrac{ Present \:Age\:of\:Ajay\: + 4 }{ Present \:Age\:of\:Vijay\: + 4 } = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \sf \dfrac{ 16\: + 4 }{ 20\: + 4 } = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \sf \dfrac{ 20 }{ 24 } = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \sf \cancel {\dfrac{ 20 }{ 24 }} = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \sf \dfrac{ 5 }{ 6 } = \dfrac{5}{6} \\\\[/tex] [tex]\qquad \longmapsto \frak{\underline{\purple{\: \dfrac{5}{6} = \dfrac{5}{6}}} }\:\:\:\bigstar \\[/tex] ⠀⠀⠀⠀⠀[tex]\therefore {\underline {\bf{ Hence, \:Verified \:}}}\\\\\\[/tex] ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Reply
❍ The Given ratio of present ages of Ajay and Vijay is 4: 5. So, Let’s say the present ages of Ajay and Vijay are 4x and 5x respectively.
☆ Four years from now their ages —
⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀
⠀⠀⠀⠀⠀
[tex]\underline{\bigstar\:\boldsymbol{According\; to \;the \;given \;Question :}}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Therefore,
⠀
[tex]:\implies\sf \bigg(\dfrac{4x + 4}{5x + 4} \bigg) = \bigg(\dfrac{5}{6}\bigg) \\\\\\:\implies\sf 6(4x + 4) = 5(5x + 4) \\\\\\:\implies\sf 24x + 24 = 25x + 20\\\\\\:\implies\sf 24x – 25x = 20 – 24 \\\\\\:\implies\sf -x = -4\\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{x = 4}}}}}\;\bigstar[/tex]
⠀
Hence,
⠀
⠀
[tex]\therefore{\underline{\sf{Hence, their\: present\;ages\:are\;\bf{16\; years\;\&\;20\:years }.}}}[/tex]
[tex]\rule{250px}{.3ex}[/tex]
⠀
V E R I F I C A T I O N :
⠀
⠀
[tex]\dashrightarrow\sf \dfrac{4x + 4}{5x + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{4(4) + 4}{5(4) + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{16 + 4}{20 + 4} = \dfrac{5}{6}\\\\\\\dashrightarrow\sf \cancel\dfrac{20}{24} = \dfrac{5}{6} \\\\\\\dashrightarrow\underline{\boxed{\frak{\dfrac{5}{6} = \dfrac{5}{6}}}}[/tex]
⠀
[tex]\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}[/tex]
⠀⠀⠀⠀⠀⠀⠀
Given : The present ages of ajay and vijay are in ratio 4:5 & four years from now their ages will be in ratio 5:6.
Exigency to find : The Present age of Ajay and Vijay .
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀
❒ Let’s consider the Present ages of Ajay and Vijay be 4x and 5x yrs , respectively .
⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:According \: to \: \: the \: Question \: \::}}\\[/tex]
⠀⠀⠀⠀⠀━━━ Four years from now the ages of Ajay and Vijay will be in ratio 5:6.
[tex]\qquad \longmapsto \sf \dfrac{ Present \:Age\:of\:Ajay\: + 4 }{ Present \:Age\:of\:Vijay\: + 4 } = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \sf \dfrac{ 4x\: + 4 }{ 5x\: + 4 } = \dfrac{5}{6} \\\\[/tex]
⠀⠀⠀⠀⠀By Cross Multiplication :
[tex]\qquad \longmapsto \sf \dfrac{ 4x\: + 4 }{ 5x\: + 4 } = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \sf 6(4x\: + 4) = 5( 5x\: + 4) \\\\[/tex]
[tex]\qquad \longmapsto \sf 24x\: + 24 = 5(5x\: + 4) \\\\[/tex]
[tex]\qquad \longmapsto \sf 24x\: + 24 = 25x\: + 20 \\\\[/tex]
[tex]\qquad \longmapsto \sf 24x\: = 25x\: + 20 – 24 \\\\[/tex]
[tex]\qquad \longmapsto \sf 24x\: = 25x\: – 4 \\\\[/tex]
[tex]\qquad \longmapsto \sf 24x\: – 25x = \: – 4 \\\\[/tex]
[tex]\qquad \longmapsto \sf -x\: = \: – 4 \\\\[/tex]
[tex]\qquad \longmapsto \sf \cancel{-} x\: = \: \cancel{-} 4 \\\\[/tex] [ “-ve” sign will be eliminated from both side]
[tex]\qquad \longmapsto \frak{\underline{\purple{\:x = 4\:yrs }} }\:\:\:\bigstar \\[/tex]
Therefore,
Therefore,
⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \sf {\:Present \:age\:of\:Ajay \:and\:Vijay \:is}\:\bf{16\:yrs \:and\:20\:yrs}\:\:\sf{,respectively}}}\\[/tex]
[tex]\rule200{1.5}[/tex]
[tex]\large {\boxed{\sf{\mid{\overline {\underline {\star \: Verification \::}}}\mid}}}\\\\[/tex]
Given that :
⠀⠀⠀⠀⠀━━━ Four years from now the ages of Ajay and Vijay will be in ratio 5:6.
[tex]\qquad \longmapsto \sf \dfrac{ Present \:Age\:of\:Ajay\: + 4 }{ Present \:Age\:of\:Vijay\: + 4 } = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \sf \dfrac{ 16\: + 4 }{ 20\: + 4 } = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \sf \dfrac{ 20 }{ 24 } = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \sf \cancel {\dfrac{ 20 }{ 24 }} = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \sf \dfrac{ 5 }{ 6 } = \dfrac{5}{6} \\\\[/tex]
[tex]\qquad \longmapsto \frak{\underline{\purple{\: \dfrac{5}{6} = \dfrac{5}{6}}} }\:\:\:\bigstar \\[/tex]
⠀⠀⠀⠀⠀[tex]\therefore {\underline {\bf{ Hence, \:Verified \:}}}\\\\\\[/tex]
⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀