Question

the difference of a two numbers is 9 and they are in the number ratio 4:7 find its number

Answer 1

$\huge\boxed{ \red{ᗩŋֆῳɛཞ}}$

Since the nos. are in ratio 4:7,therefore let the nos. be 4x and 7x.

Since the nos. are in ratio 4:7,therefore let the nos. be 4x and 7x.Now, According to given condition:7x-4x=9This gives, 3x=9 and hence x=3.

So the two numbers are 12 and 21.

Answer 2

Given : The difference of a two numbers is 9 and they are in the number ratio 4:7 .

Need To Find : The numbers .

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$\sf{\bf{ Solution \:of\:Question \::}}$ Let's consider two number be 4x and 7x .

Given that ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀The Difference between two numbers is 9 .

⠀⠀⠀⠀⠀⠀⠀⠀⠀First Number : 4x , Second number : 7x

Then ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\implies {Equation \::7x - 4x = 9 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{\underline {\bf{\star According \: To \: Question \::}}}$

Now by solving for x in Equation:

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto {Equation \::7x - 4x = 9 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto { \:7x - 4x = 9 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto { \:3x = 9 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto { \:x = \dfrac{\cancel {9}}{\cancel {3}} }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\underline {\boxed{\pink{ \:x = 3 }}}}\star$

Therefore,

• First Number is 4x = 4 × 3 = 12

• Second Number is 7x = 7 × 3 = 21

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\therefore{\sf{ \pink{ Hence ,\: The \:two \:numbers \:are\:12 \:and\:21.}}}$

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Verification :

As, We know that ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀The Difference between two numbers is 9 .

Then ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto { \:L.H.S\: = 21 }}$

⠀⠀⠀⠀⠀⠀⠀☆ Now Finding RHS using Found Value :

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto {R.H.S =\:21 - 12 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\longmapsto {R.H.S= \:9 }}$

By seeing LHS and RHS we can say that ;

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\implies {L.H.S= \:R.H.S }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\sf{\bf{\therefore {Hence, \:Verified }}}$

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