Question

Find the sum of two numbers which are in the Ratio 4:5 and their sum is 184 .​

Answer 1

Answer:

Let the numbers be x and (184-x)

⇒

3

1

x−

7

184−x

=8

⇒x=72

Thus the numbers are 72 and 112 Hence the smaller number is 72

Step-by-step explanation:

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Answer 2

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

• Find the sum of two numbers which are in the Ratio 4:5 and their sum is 180.

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

• Ratio of the Numbers = 4:5
• Sum of the Numbers = 180

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

• Let the First Number be 4x
• Let the Second Number be 5x

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

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\:4x \: + \: 5x \: = \: 180 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\bf{4x \: + \: 5x \: = \: 180 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{9x \: = \: 180 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \frac{180}{9} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \cancel\green{ \frac{180}{9}} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: 20 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 20 }}}$

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Numbers:-

• First Number = 4x = 4 × 20 = ${ \boxed{\: 80}}$
• Second Number = 5x = 5 × 20 = ${ \boxed{\: 100}}$

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\:4x \: + \: 5x \: = \: 180 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\bf{4 \times 20\: + \: 5 \times 20\: = \: 180 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{80 \: + \: 100 \: = \: 180 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{180\: = \: 180 }}}$

Hence, Verified

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ First \: Number \: = \underline {\underline{ 80}}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Second\: Number \: = \underline {\underline{ 100}}}\\\end{gathered}\end{gathered}$

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