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

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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.

Answer 2

Answer:

Sujatha Praveen

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Are the given steps to find the number true?

Step 1: Let the unit's digit be x

Step 2: Then, ten's digit =(9−x)

∴ number =10×(9−x)+x⇒90−10x+x=(90−9x)

Step 3: Adding 27 to the number 90−9x we get 117−9x

Step 4: Number with digits interchanged is 10x+(9−x)=9x+9

Step 5: 117−9x=9x+9

Step 6: Therefore unit's digit=6 and ten's digit =3

Step 7: Hence the number =36

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