Question

Present ages of Anju and Vikky are in the ratio 3:4. After 5 years from now, the ratio of their ages will be 4 : 5. Find their present ages. Q​

Answer 1

Given : Present age of Anju and Vicky are in the ratio 3:4 .After 5 years , the ratio of their ages will be 4:5 .

To Find : Find the Present Age

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SolutioN : Let's form the Equation first and after that by Cross Multiplying we can get the Present age . Let's Solve :

$\maltese$ According to the Question :

$\longmapsto$ The Present ages of Vicky and Anju are in the ratio 3:4 .So ,

$\qquad \; {\bigstar \; {\underline{\overline{\boxed{\pmb{\sf{ \; \bigg\{ \dfrac{ Anju }{ Vicky } \bigg\} = \bigg\{ \dfrac{ 3y }{ 4y } \bigg\} }}}}}}} \; \bigstar$

$\longmapsto$ After 5 years ,their ages are in the ratio 4:5 .So ,

$\qquad \; {\bigstar \; {\underline{\overline{\boxed{\pmb{\sf{ \; \bigg\{ \dfrac{ 3y + 5 }{ 4y + 5 } \bigg\} = \bigg\{ \dfrac{ 4 }{ 5 } \bigg\} }}}}}}} \; \bigstar$

$\maltese$ Cross Multiplying the Equation :

$\begin{gathered} \qquad \; \longrightarrow \; \sf { \; \bigg\{ \dfrac{ 3y + 5 }{ 4y + 5 } \bigg\} = \bigg\{ \dfrac{ 4 }{ 5 } \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \sf { 5 \bigg( 3y + 5 \bigg) = 4 \bigg( 4y + 5 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \sf { 15y + 25 = 16y + 20 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \sf { 16y - 15y = 25 - 20 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \sf { y = 25 - 20 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; {\underline{\boxed{\pmb{\frak{ y = 5 }}}}} \; {\orange{\bigstar}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Present Age :

• Anju = 3y = 3(5) = 15 years
• Vicky = 4y = 4(5) = 20 years

$\therefore \;$ Present age of Anju is 15 years and age of Vicky is 20 years .

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Answer 2

Answer:

Present age of Anju is 15 years and Vikky 20 is years.

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Given: Present ages of Anju and Vikky are in the ratio 3:4. After 5 years from now, the ratio of their ages will be 4:5.

To find: Present age of Anju and Vikky.

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Step-by-step explanation:

$\underline{\underline{\orange{\sf{As\:per\:given\:question\::}}}}$

Present ages of Anju and Vikky are in the ratio 3:4. Just the ratio of their ages is given. We don't know about their current ages. Let's call the ratio of their present ages be their current (present) age. So, present age of Anju is "3x" years and of Vikky is "4x" years.

As per second statement of the question "after 5 years from now, the ratio of their ages will be 4:5." 5 years from now on (आज से 5 साल बाद means addition) their ages will be 4:5. Simply add five years in their assumed current ages.

Add five to the ratio of current age (assumption one), so that the ratio of present ages and the ratio of ages after 5 years become the same.

$\underline{\boxed{\green{\sf{Ratio\:of\:present \:ages\: +\:5\:=\:Ratio\:of \:ages\:after\:5\: years}}}}$

Substitute the values,

$\purple {\dots\longrightarrow}{\sf{\dfrac{3x + 5}{4x + 5} =\dfrac{4}{5} }}$

Cross-multiply them,

$\purple {\dots\longrightarrow}{\sf{5({3x + 5)} = 4({4x + 5})}}$

$\purple {\dots\longrightarrow}{\sf{15x + 25 = 16x + 20}}$

$\purple {\dots\longrightarrow}{\sf{25 - 20= 16x - 15x}}$

$\purple {\dots\longrightarrow}{\sf{5= x}}$

$\purple {\dots\longrightarrow}{ \boxed{\huge\sf{x = 5}}}$

From above calculations we have value of x is 5. Now, substitute the value of x in assumed ages.

Therefore,

$\purple{\implies}{\sf{Present\:age\:of\:Anju\:=\:3(5)}}$

$\sf{=\:15\:years}$

$\purple{\implies}{\sf{Present\:age\:of\:Vikky\:=\:4(5)}}$

$\sf{=\:20\:years}$

Hence, the present age of Anju is 15 years and of Vikky is 20 years.

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Additional Information:

→ Fraction = Part/whole

There are total 8 balls out of which four are red in colour. So, here the fraction is 4/8 or 1/2.

→ Fraction = Numerator/Denominator or N/D

The given Numerator is 5 and denominator is 7. Then it's fraction is 5/7.

→ Ways of writing fraction:

• Common way = 5/2
• Decimal = 2.5
• Percentage = 250%