Question

the result of dividing a number of two digit by the number with the digit reversed is5/6.if the difference of digit is 1,find the no.​

Answer 1

Answer :

Let the two digit number be 10x + y.

Then, the number formed by reversing the digits will be 10y + x.

According to the question,

$\frac{10x + y}{10y + x} = \frac{5}{6}$

Thus,

$→6(10x + y) = 5(10y + x) \\ \\ →60x + 6y = 50y + 5x \\\\→ 60x - 5x =50y - 6y \\ \\ →55x = 44y \\ \\→ x = \frac{4y}{5} .................eq1$

And,

Difference between the two digits = 1

Hence, x - y = 1 .................... eq2

Now,

Using eq1 in eq2, we get

$→x - y = 1 \\\\ →\frac{4y}{5} - y = 1 \\\\ → \frac{4y - 5y}{5} = 1 \\\\ → -\frac{y}{1} = 5\\ \\→ y = -5$

Hence, if y = -5 then

x - y = 1

x - (-5) = 1

x = 1 - 5 = -4

Therefore, the two digit number is 10x+y = (-45).

Answer 2

$\huge\red{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Number \ is \ -45.}$

$\huge\sf\purple{Given:}$

➡$\sf{The \ result \ of \ dividing \ a \ number}$

$\sf{of \ two \ digit \ by \ the \ number \ with}$

$\sf{the \ reversed \ is \ \frac{5}{6}.}$

➡$\sf{The \ difference \ between \ the \ digits}$

$\sf{is \ 1.}$

$\huge\sf\blue{To \ find:}$

$\sf{The \ number.}$

$\huge\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ digit \ in \ the \ ten's \ place \ of }$

$\sf{number \ be \ x \ and \ in \ units \ place \ be \ y.}$

$\sf{\therefore{Original \ number=10x+y}}$

$\sf{Number \ with \ reversed \ digit's=10y+x}$

$\sf{According \ to \ the \ first \ condition}$

$\sf{\frac{10x+y}{10y+x}=\frac{5}{6}}$

$\sf{5(10y+x)=6(10x+y)}$

$\sf{50y+5x=60x+6y}$

$\sf{60x-5x+6y-50y=0}$

$\sf{55x-44y=0}$

$\sf{11(5x-4y)=0}$

$\sf{5x-4y=\frac{0}{11}}$

$\sf{5x-4y=0...(1)}$

$\sf{According \ to \ the \ second \ condition}$

$\sf{x-y=1...(2)}$

$\sf{Multiply \ eq(2) \ 4, \ we \ get}$

$\sf{4x-4y=4...(3)}$

$\sf{Subract \ equation \ (3) \ from \ (1)}$

$\sf{5x-4y=0}$

$\sf{-}$

$\sf{4x-4y=4}$

_________________

$\sf{x=-4}$

$\sf{Substitute \ x=-5 \ in \ eq(2), \ we \ get}$

$\sf{-4-y=1}$

$\sf{-y=1+4}$

$\sf{-y=5}$

$\sf{\therefore{y=-5}}$

$\sf{The \ number=10x+y}$

$\sf{=10×(-4)+(-5)}$

$\sf{=-40-5}$

$\sf{=-45}$

$\sf\purple{\tt{\therefore{Number \ is \ -45.}}}$