Question

two numbers are such that the ratio between them is 3: 5 if each is increased by 10 the ratio between the new number so formed is 5:7 find the original number​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• Two numbers are such that the ratio between them is 3: 5. If each is increased by 10 the ratio between the new number so formed is 5:7 . Find the original number

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$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

Since , the Ratio is between the Numbers is 3:5

• $\sf\green{ Let\: the \: two \: numbers \: be \: \fbox \red{3x} \: and \: \fbox \red{5x} }$

If each number is increased by 10 , then the new number are

• $\blue{\fbox\orange{3x \: + \: 10 }}$
• $\blue{\fbox\orange{5x \: + \: 10 }}$

$\red{\boxed{ \sf \blue{ Ratio \: of \: New \: Number \: = \:\green{\fbox \orange{5:7}} }}}$

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Question :}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \frac{3x \: + \: 10}{5x \: + \: 10} \: = \: \frac{5}{7} }} }\\ \end{gathered}\end{gathered}\end{gathered}$

By Cross Multiplaction

$\quad {:} \longrightarrow \sf{\sf{7 \: (3x + 10) \: = \: 5 \: (5x + 10) }}$

$\quad {:} \longrightarrow \sf{\sf{21x \: + \: 70 \: = \: 25x \: + \: 50 }}$

$\quad {:} \longrightarrow \sf{\sf{21x \: - \:25x \: = \: -70\: + \: 50 }}$

$\quad {:} \longrightarrow \sf{\sf{-4x \: = \: -20 }}$

$\quad {:} \longrightarrow \sf{\sf{x \: = \: \cancel{ \frac{ - \: 20}{ - \: 4} } }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ x \: = \: 5 }}}$

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First Number = 3x = 3 × 5 = 15

Second Number = 5x = 5 × 5 = 25

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Answer 2

Answer:

Two numbers are such that the ratio between them is 3: 5. If each is increased by 10 the ratio between the new number so formed is 5:7 . Find the original number

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Step-by-step explanation:

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