Question

The fraction obtained by dividing a two digit number by the number obtained by reversing the digits is 8/3. The sum of the number is 9. Find the original number.​

Answer 1

HERE'S YOUR ANSWER....✌️✌️

HERE'S YOUR ANSWER....✌️✌️The equation is ,

HERE'S YOUR ANSWER....✌️✌️The equation is ,x+y =9........(i)

HERE'S YOUR ANSWER....✌️✌️The equation is ,x+y =9........(i)10x + y = (10y + x)-9 ........(ii)

HERE'S YOUR ANSWER....✌️✌️The equation is ,x+y =9........(i)10x + y = (10y + x)-9 ........(ii)the original number is 10x + y

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a number which when divided by the number obtained by reversing its digit gives a fraction 8/3
• Sum of digits of number is 9

To Find:

• We have to find the original number

Solution:

Let Tens digit of number = x

Unit digit of number = y

$\boxed{\sf{Original \: Number = 10x + y}}$

Given that sum of digit is 9

$\implies \sf{x + y = 9}$

$\implies \boxed{\sf{y = 9 - x }}$ ---------- 1

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$\underline{\large\mathfrak\red{According \: to \: the \: Question:}}$

The fraction obtained by dividing a two digit number by the number obtained by reversing the digits is 8/3

$\implies \boxed{\bold{\dfrac{\text{Original \: Number}}{\text{Reversed \: Number }} = \dfrac{8}{3}}}$

$\implies \sf{\dfrac{10x + y}{10y+x} = \dfrac{8}{3} }$

Cross Multiplying the Terms

$\implies \sf{3 \: ( 10x + y ) = 8 \: ( 10y + x ) }$

$\implies \sf{30x + 3y = 80y + 8x}$

$\implies \sf{30x - 8x = 80y - 3y}$

$\implies \sf{22x = 77y}$

$\implies \sf{2x = 7y}$

Substituting the values of y from Equation 1

$\implies \sf{2x = 7 \: ( 9 - x ) }$

$\implies \sf{2x = 63 - 7x}$

$\implies \sf{9x = 63 }$

$\implies \sf{x = \dfrac{63}{9}}$

$\implies \boxed{\sf{x = 7}}$

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Putting x = 7 in Equation 1 , we get

$\implies \sf{y = 9 - 7}$

$\implies \boxed{\sf{y = 2}}$

Original number is as follows :

$\implies \sf{10 \: (7) + 2}$

$\implies \sf{70 + 2}$

$\implies \sf{72 }$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s} \pink{w} \blue{e}\purple{r}} }$

$\large\boxed{\sf{Original \: Number = 72}}$

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$\huge\mathtt\green{Verification:}$

☞ The fraction obtained by dividing a two digit number by the number obtained by reversing the digits is 8/3

➬$\sf{Fraction = \dfrac{72}{27}}$

➬$\sf{Fraction = \dfrac{8}{3}}$

$\large\red{\underline{\underline{\sf{Hence \: Verified \: !!! }}}}$