Question

HOTS:
A number has two digits whose sum is 9. If 27 is added to the
number, its digits get interchanged. Find the number.
THint: Let the digits in the units place be x... The digits in the tens place​

Answer 1

okay first let me tell you this is the problem from linear equation chapter..

Step-by-step explanation:

let the digit in unit place be x

let the digit in tens place be y

then sum of these number is 9.

10y+x=9 --------(1)

next adding 27 the number get reversed

so,

once place will be y

and tens place be x

10x+y=27 --------(2)

now by elimination method,

10x+y=27 multiply by 10

x+10y=9

so the then equation will be,

100x+10y= 270

-(x+10y=9)

-------------------------

99x =261

continue finding x and then substitute the value of x in any one equation and u will get y

then put x and y together then u will get the numbers....

sorry for not doing the full thing

battery is abt to die

but have explained the whole process......

Answer 2

$\boxed{ \huge{ \fcolorbox{yellow}{white}{ \pink{Solution}}} }$

Let the units of the number be x.

Then,the digit in the ten place =( 9 - x )

$Number = 10×(9-x)+x$

$=90-10x+x=(90-9x).$

The number with its digits interchanged = 10x+(9-x)= ( 9x + x ).

$Hence, (90 - 9x) + 27 = 9x + 9$

$= > 117 - 9x = 9x + 9$

$= > 18x = 108$

$= > x = \frac{108}{18} = 6.$

Thus, the digit in the units place =6 and the digit in the tens place =3.

Hence, the no. is 36.