Question

A number consists of two digits whose sum is 9 . If 9 is subtracted from the number the digit interchanged their places . Find the number

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us assume that , the given two digit number is 10x + y .

Given That,

→ x + y = 9 ---------------- Eqn(1)

Also,

→ (10x + y) - 9 = (10y + x)

→ 10x - x + y - 10y = 9

→ 9x - 9y = 9

→ 9(x - y) = 1

→ (x - y) = 1 ----------------- Eqn(2)

Adding Both Eqn. we get,

→ (x + y) + (x - y) = 9 + 1

→ x + x + y - y = 10

→ 2x = 10

→ x = 5 .

Putting This value in Eqn(1) Now, we get,

→ 5 + y = 9

→ y = 9 - 5

→ y = 4

Hence, The Required Original Two - digit Number is = 10x + y = 10*5 + 4 = 50 + 4 = 54 (Ans.)

Answer 2

$\huge{\tt{\underline{\tt{\: Solution:-}}}}$

${\tt{Let \: assume \: the \: given\: digit \: number \: is \: 10x+y}}$

${\tt{Given:-}}$

${\tt{ x- y = 9}}-----eq (1)$

Now,

${\tt{(10x + y) -9 =(10y +x)}}$

${\tt{10x - x + y - 10y = 9)}}$

${\tt{9(x + y) = 1}}$

${\tt{ x- y = 1}}-----eq (2)$

${\tt{\underline{\pink{\: Adding\: both \: equation\: we \: get, :-}}}}$

${\implies{\tt{(x + y) + (x-y) = 9 +1 }}}$

${\implies{\tt{x + x + y - y = 10}}}$

${\implies{\tt{2x = 10}}}$

${\implies{\tt{x = \cancel\frac{10}{2} = 5}}}$

${\implies{\tt{x = 5}}}$

${\red{\tt{putting\: this \: value \: in \: eq(1), \: we\: get, }}}$

${\implies{\tt{5+ y = 9}}}$

${\implies{\tt{y = 9 -5 }}}$

${\implies{\tt{4}}}$

${\red{\tt{\therefore{The \:required \: two\: original\: digits\: number \: is \: = 10 + y =10 ×5 + 4 = 50 + 4 =54}}}}$