Question

A two digit number is such that the sum of digits is 4. If 8 is added to the number its digits are reversed find the number.​

Answer 1

Step-by-step explanation:

All 2-digit numbers are in the form 10a+b

The following 2 equations are derived from the question:

10a+b = 4(a+b)

10a+b+18=10b+a

Let’s simplify the first equation:

10a+b = 4(a+b)

10a+b = 4a+4b

6a = 3b

2a = b

Now, we know the possible values of a and b:

[a=1, b=2], [a=2, b=4], [a=3, b=6], [a=4, b=8]

Now, we can use trial and error with the second equation, by substituting in the possible values of a and b:

[a=1, b=2]: 12 + 18 ≠ 21

[a=2, b=4]: 24 + 18 = 42

Above is a number which fulfills the requirements, 24. However, we must check to be sure that there are no other possible solutions.

[a=3, b=6]: 36 + 18 ≠ 63

[a=4, b=8]: 48 + 18 ≠ 84

The above values of a and b do not fulfill the requirements.

The number is of form 10a+b where a=2 and b=4, so the number is 24

Answer 2

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