Question

pls solve ... it's urgent...

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Answer 1

Let the digit be 10x+y

where x+y=7...(1)

when digits are interchanged.

it become 10y+x

Given: 10y+x-(10x+y)=9

10y+x-10x-y=9

9y-9x=9

y-x=1... (2)

Solving (1) and (2) simultaneously y=4 and x=3

so number=10x+y

10 (3)+4

30+4=34.

Step-by-step explanation:

Answer 2

$\underline{\underline{To\:Find}}$

The original Number..

$\underline{\underline{Given:}}$

Sum of digits = 7

$\therefore a + b = 7$[Equation.....(i)]

It is given that when the digits are interchanged ,the no. is decreased by..9.

$\underline{\underline{Taken}}$

Let the no. be (10a + b) and no. obtained on reversing the digits be (10b + a).

$\therefore 10b + a - (10a + b) = 9$

By solving it , we get;

$\Rightarrow 10b + a - 10a - b = 9$

$\Rightarrow (9b - 9a) = 9$

$\Rightarrow 9(b - a) = 9$

$\Rightarrow (b - a) = 1$

$b - a = 1$[Equation...(ii)]

______________________________________

$\underline{\underline{Solution:}}$

Putting the two equations together, we get;

a + b = 7

-a + b = 1

_______[By Adding]

2b = 8

b = 4.

putting the value in the equation 1, we get;

a + (4) = 7

a = 7 - 4

a = 3.

Hence , the number is 10(3) + 4 = 34..

${\boxed{Original\:no. = 34}}$