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The sum of a two-digit number and the number formed by interchanging the two digits is 45 more than twice the original number. If the sum of the digits of the number is 9, what is the original number?
- a)72
- b)36
- c)63
- d)18
- e)27
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
The sum of a two-digit number and the number formed by interchanging t...
Let the original two digit number be xy. 10x + y + l0y + x = 40 + 2(10x + y)
11x + 1 ly = 45 + 20x + 2y
9y - 9x = 45
y-x = 5 ... (I)
Also, y + x = 9 ... (II)
Solving (I) and (II), y = 7 and x = 2 Hence, the original number is 27.
Hence, option 5.
Hence, option 5.
Most Upvoted Answer
The sum of a two-digit number and the number formed by interchanging t...
Given:
- The sum of a two-digit number and the number formed by interchanging the two digits is 45 more than twice the original number.
- The sum of the digits of the number is 9.
To find:
The original number.
Solution:
Let's assume the original number is AB, where A is the tens digit and B is the units digit.
Sum of the two-digit number and the number formed by interchanging the digits:
The number formed by interchanging the digits is BA.
So, the sum of the two-digit number and the number formed by interchanging the digits is AB + BA = 10A + B + 10B + A = 11A + 11B = 11(A + B).
Given that the sum of the two-digit number and the number formed by interchanging the digits is 45 more than twice the original number:
11(A + B) = 2(10A + B) + 45
11A + 11B = 20A + 2B + 45
11A - 20A = 45 - 11B
-9A = 45 - 11B
9A = 11B - 45
Given that the sum of the digits of the number is 9:
A + B = 9
Substitute the value of A from the second equation into the first equation:
9(11B - 45) = 11B - 45
99B - 405 = 11B - 45
99B - 11B = 405 - 45
88B = 360
B = 360/88
B ≈ 4.09
Since B is a digit, B ≈ 4.
Substitute the value of B into the equation A + B = 9:
A + 4 = 9
A = 9 - 4
A = 5
Therefore, the original number is 54.
Hence, the correct answer is option E.
- The sum of a two-digit number and the number formed by interchanging the two digits is 45 more than twice the original number.
- The sum of the digits of the number is 9.
To find:
The original number.
Solution:
Let's assume the original number is AB, where A is the tens digit and B is the units digit.
Sum of the two-digit number and the number formed by interchanging the digits:
The number formed by interchanging the digits is BA.
So, the sum of the two-digit number and the number formed by interchanging the digits is AB + BA = 10A + B + 10B + A = 11A + 11B = 11(A + B).
Given that the sum of the two-digit number and the number formed by interchanging the digits is 45 more than twice the original number:
11(A + B) = 2(10A + B) + 45
11A + 11B = 20A + 2B + 45
11A - 20A = 45 - 11B
-9A = 45 - 11B
9A = 11B - 45
Given that the sum of the digits of the number is 9:
A + B = 9
Substitute the value of A from the second equation into the first equation:
9(11B - 45) = 11B - 45
99B - 405 = 11B - 45
99B - 11B = 405 - 45
88B = 360
B = 360/88
B ≈ 4.09
Since B is a digit, B ≈ 4.
Substitute the value of B into the equation A + B = 9:
A + 4 = 9
A = 9 - 4
A = 5
Therefore, the original number is 54.
Hence, the correct answer is option E.
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The sum of a two-digit number and the number formed by interchanging the two digits is 45 more than twice the original number. If the sum of the digits of the number is 9, what is the original number?a)72b)36c)63d)18e)27Correct answer is option 'E'. Can you explain this answer?
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