3) The sum of the digits of a two digit number is 9. The number formed
by reversing the digits is greater than the original number by 9. Find
the original number.
Answers
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).
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.
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.
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.hope this will be helpful to you and please mark my answer as the brainleast answer
Answer:
Original No. is 45
Explanation:
Let the digits in two digit no. are x and y
Acc. to statement,
x + y = 9
y = 9 - x
Original no. = 10y + x = 10( 9 - x) + x
Now,
10x + y = 10y + x + 9
10x + 9 - x = 10(9 - x) + x + 9
9x + 9 = 90 - 10x + x + 9
9x + 9 = 99 - 9x
9x + 9x + 9 - 99 = 0
18x - 90 = 0
18x = 90
x = 90/ 18
x = 5
also, y = 9 - 5 = 4
Therefore, the original no. = 10y + x = 40 + 5 = 45