Question

The sum of digits of a two-digit number is 8. If 36 is added to this number , the digits are reserved. Find the number

Answer 1

$<b>Heya mate. (^_-). Solution below.$
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[] Let the ten's digit be 'x' and unit's digit be 'y'.

[] Then, it is given that,

x + y = 8... [equation i]

[] Now, the two digit number = 10x + y

And, number formed by interchanging its digits = 10y + x

[] Now, according to the question, if 36 is added to original number, it's digits get reversed.

or, 10x + y + 36 = 10y + x

=> 10x + y - 10y - x = - 36

=> 10x - x - 10y + y = -36

=> 9x - 9y = -36

=> 9 (x - y) = -36

=> x - y = -36/9

=> x - y = -4.... [equation ii]

[] Now, adding equations i and ii,

x + y = 8

x - y = -4
(+) (+) (+)

=> 2x = 4 (y and -y get cancelled)

=> x = 4/2

=> x = 2

•°• x = 2

[] Now, substituting the value of x in equation i,

x + y = 8

=> 2 + y = 8

=> y = 8 - 2

=> y = 6

•°• y = 6

[] Therefore, the number,

= 10x + y

= 10(2) + 6

= 20 + 6

= 26

$<marquee>Hence, the number is 26.</marquee>$
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$<u>Verification -</u>$


[] The number = 26


=>> Sum of digits
= 2 + 6
= 8


=>> When 36 added,
= 26 + 36
= 62 (digits are interchanged)

Hence verified.
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Thank you... ;-)

Answer 2

Hi there!
Here's the answer:

•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°


¶¶¶ SOLUTION

In two digit Number,
Let Unit digit be x
& Tens digit be 8-x
( Given that Sum of digits = 8 )


Number = (10 × face Value of Tens place ) + (1 × face Value of Units place)

•°•
Original No. = 10(8-x) + x


Given,
Digits are interchanged if 36 is added to this No.

^^ New No. = 10x + (8-x)


=> [10(8-x) + x] + 36 = 10x + (8-x)

=> 80-10x+x+36 = 10x + 8 -x
=> 116 -9x = 9x + 8
=> 9x + 9x = 116 - 8
=> 18x = 108
=> x = 6

•°• Units Digit = x = 6
& Tens Digit = 8-x = 2

•°• Required No. = 26


•°•°•°•°•°•<><><<><>><><>•°•°•°•°•°


¶¶¶ VERIFICATION:

Original No. = 26

• Sum of digits = 8

26 + 36 = 62

• - Original No. Digits are Interchanged --

•°• Given Data Matched