Question

The digits of two digit number differ by 3.If the digits are interchanged and two numbers are added, their sum is 77.Find the numbers.

Answer 1

Here is your answer

$\rule{135}{2}$

Let the digit at units place be x

Let the digit at tens place be x + 3

10(x + 3) + x

When digits interchanged, the number becomes 10x + x + 3

According to the question,

10(x + 3) + x + 10x + x + 3 = 77

10x + 30 + 12x + 3 = 77

22x + 33 = 77

22x = 77 - 33

22x = 44

x = $\frac{44}{22}$

x = 2

∴ The number = 10(x + 3) + x = 10 * 5 + 3 + 5 = 50 + 3 + 5 = 53 + 5 = 58

∴ The number is 58

Answer 2

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


[] Then, it is given

x - y = 3... [equation i]



[] Now, the original number = 10x + y



[] Number obtained by interchanging its digits = 10y + x




[] Now, according to the question, the sum of both the numbers is 77

=>> 10x + y + 10y + x = 77

=> 11x + 11y = 77

=> 11 (x + y) = 77

=> x + y = 77/11

=> x + y = 7... [equation ii]



[] Now, adding equations i and ii,


x - y = 3

x + y = 7
(+) (+) (+)


=>> 2x = 10 (y and -y get cancelled)

=> x = 10/2

=> x = 5

•°• x = 5



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

x - y = 3

=> 5 - y = 3

=> 5 - 3 = y

=> 2 = y

•°• y = 2



[] Therefore, original number,

= 10x + y

= 10(5) + 2

= 50 + 2

= 52


[] And, number obtained by interchanging its digits,

10y + x

= 10(2) + 5

= 20 + 5

= 25


$<marquee>Hence, the numbers are 52 and 25.</marquee>$
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$<u>Verification -</u>$

[] The number is 52,


• Difference between the number,

= 5 - 2

= 3


• Sum of original number and number obtained by interchanging the digits,

= 52 + 25

= 77.


Hence verified.
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Thank you... ;-)