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The difference between the digits of a two-digit number is 3. If the digits are interchanged and the resulting number is added to the original number we get 143. What was the original number?
- a)58
- b)85 9
- c)78
- d)87
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The difference between the digits of a two-digit number is 3. If the d...
Let the unit’s digit be x.
Ten’s digit = x + 3.Original number =10(x + 3) + 1(x)
= 10x + 30 + x
= 11x + 30
After interchange, resulting number
= 10 (x) + 1 (x + 3)
= 10x + x + 3
= 11x + 3
∴ 11x + 3 + 11x + 30 = 143
⇒ 22x + 33 = 143
⇒ 22x = 143 – 33
⇒ 22x = 110
⇒
Original number = 11x + 3 = 11 × 5 + 3
= 55 + 3 = 58
Ten’s digit = x + 3.Original number =10(x + 3) + 1(x)
= 10x + 30 + x
= 11x + 30
After interchange, resulting number
= 10 (x) + 1 (x + 3)
= 10x + x + 3
= 11x + 3
∴ 11x + 3 + 11x + 30 = 143
⇒ 22x + 33 = 143
⇒ 22x = 143 – 33
⇒ 22x = 110
⇒
Original number = 11x + 3 = 11 × 5 + 3
= 55 + 3 = 58
Most Upvoted Answer
The difference between the digits of a two-digit number is 3. If the d...
**Problem Analysis:**
Let's assume the original two-digit number is xy, where x represents the tens digit and y represents the units digit. According to the given information, the difference between the digits is 3. This can be written as:
x - y = 3 ---(1)
When the digits are interchanged, the resulting number is yx. If this number is added to the original number xy, we get 143. Mathematically, this can be represented as:
xy + yx = 143 ---(2)
We need to find the original number xy.
**Solution:**
To solve this problem, we can use a systematic approach. Let's consider all the possible values for x and y and check if they satisfy both equations (1) and (2).
Let's start with the possible value of x. Since x represents the tens digit, it can only take values from 1 to 9 (excluding 0).
Case 1: x = 1
If x = 1, then y = 1 + 3 = 4 (from equation 1).
The original number xy = 14.
Interchanging the digits, we get yx = 41.
Adding the original number and the interchanged number, we get 14 + 41 = 55, which is not equal to 143.
Case 2: x = 2
If x = 2, then y = 2 + 3 = 5 (from equation 1).
The original number xy = 25.
Interchanging the digits, we get yx = 52.
Adding the original number and the interchanged number, we get 25 + 52 = 77, which is not equal to 143.
Case 3: x = 3
If x = 3, then y = 3 + 3 = 6 (from equation 1).
The original number xy = 36.
Interchanging the digits, we get yx = 63.
Adding the original number and the interchanged number, we get 36 + 63 = 99, which is not equal to 143.
Case 4: x = 4
If x = 4, then y = 4 + 3 = 7 (from equation 1).
The original number xy = 47.
Interchanging the digits, we get yx = 74.
Adding the original number and the interchanged number, we get 47 + 74 = 121, which is not equal to 143.
Case 5: x = 5
If x = 5, then y = 5 + 3 = 8 (from equation 1).
The original number xy = 58.
Interchanging the digits, we get yx = 85.
Adding the original number and the interchanged number, we get 58 + 85 = 143, which is equal to 143.
Therefore, the original number is 58, which matches option A.
Let's assume the original two-digit number is xy, where x represents the tens digit and y represents the units digit. According to the given information, the difference between the digits is 3. This can be written as:
x - y = 3 ---(1)
When the digits are interchanged, the resulting number is yx. If this number is added to the original number xy, we get 143. Mathematically, this can be represented as:
xy + yx = 143 ---(2)
We need to find the original number xy.
**Solution:**
To solve this problem, we can use a systematic approach. Let's consider all the possible values for x and y and check if they satisfy both equations (1) and (2).
Let's start with the possible value of x. Since x represents the tens digit, it can only take values from 1 to 9 (excluding 0).
Case 1: x = 1
If x = 1, then y = 1 + 3 = 4 (from equation 1).
The original number xy = 14.
Interchanging the digits, we get yx = 41.
Adding the original number and the interchanged number, we get 14 + 41 = 55, which is not equal to 143.
Case 2: x = 2
If x = 2, then y = 2 + 3 = 5 (from equation 1).
The original number xy = 25.
Interchanging the digits, we get yx = 52.
Adding the original number and the interchanged number, we get 25 + 52 = 77, which is not equal to 143.
Case 3: x = 3
If x = 3, then y = 3 + 3 = 6 (from equation 1).
The original number xy = 36.
Interchanging the digits, we get yx = 63.
Adding the original number and the interchanged number, we get 36 + 63 = 99, which is not equal to 143.
Case 4: x = 4
If x = 4, then y = 4 + 3 = 7 (from equation 1).
The original number xy = 47.
Interchanging the digits, we get yx = 74.
Adding the original number and the interchanged number, we get 47 + 74 = 121, which is not equal to 143.
Case 5: x = 5
If x = 5, then y = 5 + 3 = 8 (from equation 1).
The original number xy = 58.
Interchanging the digits, we get yx = 85.
Adding the original number and the interchanged number, we get 58 + 85 = 143, which is equal to 143.
Therefore, the original number is 58, which matches option A.
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The difference between the digits of a two-digit number is 3. If the digits are interchanged and the resulting number is added to the original number we get 143. What was the original number?a)58b)85 9c)78d)87Correct answer is option 'A'. Can you explain this answer?
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