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The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. Find the number.
- a)42
- b)53
- c)17
- d)71
- e)None
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The sum of the digits of a two-digit number is 8. If the digits are re...
Let the units number be u; the tens be t.
A) t+u=8
B) 10u+t=10t+u+54
.
A) u=8-t
B)
10(8-t)+t=10t+8-t+54
80-10t+t=9t+62
80-9t=9t+62
18t=18
t=1
u=7
The number is 17.
Most Upvoted Answer
The sum of the digits of a two-digit number is 8. If the digits are re...
Given:
- The sum of the digits of a two-digit number is 8.
- If the digits are reversed, the number is decreased by 54.
To find: The two-digit number.
Let's assume the tens digit of the number to be 'x' and the units digit to be 'y'.
The number can be represented as: 10x + y
According to the first condition,
x + y = 8 ----(1)
According to the second condition,
10y + x = 10x + y - 54
Simplifying the above equation, we get
9y - 9x = -54
Dividing by 9 on both sides, we get
y - x = -6 ----(2)
Adding equations (1) and (2), we get
2y = 2
y = 1
Substituting the value of y in equation (1), we get
x + 1 = 8
x = 7
Therefore, the number is 10x + y = 71.
Hence, the correct option is (d) 71.
- The sum of the digits of a two-digit number is 8.
- If the digits are reversed, the number is decreased by 54.
To find: The two-digit number.
Let's assume the tens digit of the number to be 'x' and the units digit to be 'y'.
The number can be represented as: 10x + y
According to the first condition,
x + y = 8 ----(1)
According to the second condition,
10y + x = 10x + y - 54
Simplifying the above equation, we get
9y - 9x = -54
Dividing by 9 on both sides, we get
y - x = -6 ----(2)
Adding equations (1) and (2), we get
2y = 2
y = 1
Substituting the value of y in equation (1), we get
x + 1 = 8
x = 7
Therefore, the number is 10x + y = 71.
Hence, the correct option is (d) 71.
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