Question

Sum of the three number is 102,if the ratio between first and second be 2:3 and that between second and third be 5:3 then the second number is​

Answer 1

${\pmb{\underline{\sf{Required \ Solution ... }}}}$

• Sum of the three number is 102
• Ratio b/w first and second be 2:3
• Ratio b/w second and third be 5:3

Let the ${\sf{ 1^{st} , 2^{nd} \ and \ 3^{rd} }}$ be x, y and z.

• x + y + z = 102

As We know that:

$\colon\implies{\sf{ 3x = 2y }} \\ \\ \colon\implies{\sf{x = \dfrac{2y}{3} \ \ \ \ \ \cdots(1) }}$

We also Know that:

$\colon\implies{\sf{ 3y = 2z }} \\ \\ \colon\implies{\sf{z = \dfrac{3y}{5} \ \ \ \ \ \cdots(2) }}$

$\circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\Rightarrow{\sf{ x + y + z = 102 }} \\ \\ \colon\Rightarrow{\sf{ \dfrac{2y}{3} + y + \dfrac{3y}{5} = 102 }} \\ \\ \\ \colon\Rightarrow{\sf{ \dfrac{10y+15y+9y}{15} = 102 }} \\ \\ \\ \colon\Rightarrow{\sf{ \dfrac{34y}{15} = 102 }} \\ \\ \\ \colon\Rightarrow{\sf{ 34y = 102 \times 15 }} \\ \\ \\ \colon\Rightarrow{\sf{ y = \dfrac{ \cancel{102} \times 15}{ \cancel{34} } }} \\ \\ \\ \colon\Rightarrow{\sf{ y = 3 \times 15 }} \\ \\ \colon\implies{\underline{\boxed{\sf{y = 45 }}}}$

Hence,

${\pmb{\underline{\sf\red{ The \ second \ number \ is \ 45 . }}}}$

Answer 2

ʀᴇǫᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ-:

⇝Let the first , second and third number be x,y and z

⇝The ratio between first and second be 2:3

⇢So,$\begin{gathered}\sf\frac{x}{y}=\sf\frac{2}{3}\sf{x}=\sf\frac{2}{3}y\end{gathered}$

⇝The ratio between second and third be 5:3

⇢So,$\begin{gathered}\sf\frac{y}{z}=\sf\frac{5}{3}\sf{z}=\sf\frac{3}{5}y\end{gathered}$

⇝The sum of three numbers is 102.

⇢So, $\sf\frac{2}{3}y+y+\sf\frac{3}{5}y$

⇢$\sf\frac{34}{15}y$ = $\sf102$

⇢y = $\sf{102}×\sf\frac{15}{34}$

⇢y = 45

Hence the second number is 45

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