Sum of the digit of a two number is 9 when we interchange the digit, it is found that the resulting new number is greater than the original number by 27. What is the two digit number
Answers
Answer:
number is 9 when we interchange the digit, it is found that the resulting new numbers
Step-by-step explanation:
number is greater than the original
Answer:
36
Step-by-step explanation:
Suppose the number is ab, where a and b are single digit integers in [0,9]. So, the original number is ab = 10a+b and the number with “interchanged” digits is ba = 10b+a. According to the original statement, we have (10b+a)-(10a+b) >= 27. Simplifying it yields b-a>=3 (i.e., b >= a + 3).
Because a+b = 9, we also have a = 9-b and hence b >= a + 3 = (9-b)+3 = 12 - b, which implies that b >= 6. Because a + b = 9, we also have a <= 3.
Finally, we simply verify the number of ab, where a <= 3 and b >= 6, to see which one would satisfy the required conditions. Then, the answer is a = 3 and b = 6, and the desired number is 36.
This is a very boring answer, but it provides you with all the ingredients. :-)
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