Question

the ratio of present ages of priya and tanu is 4 : 5 , section after 8 years the ratio of their ages will be 5 : 6, find their present age.​

Answer 1

Given : The ratio of present age of Priya and Tanu is 4:5 ,after 8 years the ratio of their ages will be 5:6 .

To Find : Find the Present age

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN : In this question ,we need to form the Equation according to the Question .Than, we can calculate the ages .Let's Solve :

$\maltese$ According to the Question :

$\longmapsto$ Ratio of the Present age is 5:6 .So,

$\qquad \; \bigstar \; {\underline{\overline{\boxed{\sf{ \dfrac{Age \; of \; Priya}{Age \; of \; Tanu} = \dfrac{4y}{5y} }}}}} \; \bigstar$

$\longmapsto$ After 8 years, the ratio of their ages will be 5:6 .So,

$\qquad \; \bigstar \; {\underline{\overline{\boxed{\sf{ \dfrac{4y + 8}{5y + 8} = \dfrac{5}{6} }}}}} \; \bigstar$

$\maltese$ Cross - Multiplying the Equation :

$\begin{gathered} \; \dashrightarrow \; \; \sf { \dfrac{4y + 8}{5y + 8} = \dfrac{5}{6} } \\ \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 5 \bigg( 5y + 8 \bigg) = 6 \bigg( 4y + 8 \bigg) } \\ \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 25y + 40 = 24y + 48 } \\ \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { 25y - 24y = 48 - 40 } \\ \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { y = 48 - 40 } \\ \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak{ y = 8 }}}}} \; {\red{\bigstar}} \end{gathered}$

$\maltese$ Calculating the Ages :

• Age of Priya = 4y = 4(8) = 32 years
• Age of Tanu = 5y = 5(8) = 40 years

$\maltese$ Therefore :

Present age of Priya is 32 years and age of Tanu is 40 years .

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Answer 2

$\pink{Let \: ages \: if \: them \: be \: 4x \: and \: 5x \: according \: to \: Question: 4x + 8 + 5x + 8 = 5x + 6x} \\ \pink{9x + 16 = 11x} \\ \pink{11x - 9x = 16} \\ \pink{2x = 16} \\ \pink{ x = \frac{16}{2} } \\ \pink{x = 8} \\ \pink{present \: age \: of \: anu = 4x = 4 \times 8 = 32 }\\ \pink{present \: age \: of \: raj = 5x = 5 \times 8 = 40}$