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The sum of the digits of two-digit number is 14 and the difference between the two digits number is 2. What is the product of the two digits of the two-digit number ?
- a)56
- b)48
- c)45
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The sum of the digits of two-digit number is 14 and the difference bet...
Let be the ten's digit be x and unit's digit be y.
So the two digit number = 10x + y ( where x > y )
According to question
x + y = 14 ....(i)
x - y = 2 ....(ii)
So the two digit number = 10x + y ( where x > y )
According to question
x + y = 14 ....(i)
x - y = 2 ....(ii)
Solving Eqs. (i) and (ii), we get
x = 8 and y = 6
∴ Required product = 8 x 6 = 48
x = 8 and y = 6
∴ Required product = 8 x 6 = 48
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Community Answer
The sum of the digits of two-digit number is 14 and the difference bet...
Understanding the Problem
To solve for the two-digit number where the sum of the digits is 14 and the difference between the digits is 2, we can denote the digits as follows:
- Let the tens digit be x.
- Let the units digit be y.
Setting Up the Equations
From the problem statement, we can derive two key equations:
1. The sum of the digits:
x + y = 14
2. The difference between the digits:
x - y = 2
Solving the Equations
Now, we can solve these equations step by step.
- From the first equation (sum):
y = 14 - x
- Substituting y in the second equation (difference):
x - (14 - x) = 2
Simplifying this gives:
2x - 14 = 2
2x = 16
x = 8
- Finding y:
Substitute x back into the equation for y:
y = 14 - 8 = 6
Identifying the Digits
Thus, the digits of the two-digit number are:
- Tens digit (x) = 8
- Units digit (y) = 6
Finding the Product
Now, we calculate the product of the two digits:
- Product = x * y = 8 * 6 = 48
Conclusion
Therefore, the product of the two digits of the two-digit number is 48, confirming that the correct answer is option 'B'.
To solve for the two-digit number where the sum of the digits is 14 and the difference between the digits is 2, we can denote the digits as follows:
- Let the tens digit be x.
- Let the units digit be y.
Setting Up the Equations
From the problem statement, we can derive two key equations:
1. The sum of the digits:
x + y = 14
2. The difference between the digits:
x - y = 2
Solving the Equations
Now, we can solve these equations step by step.
- From the first equation (sum):
y = 14 - x
- Substituting y in the second equation (difference):
x - (14 - x) = 2
Simplifying this gives:
2x - 14 = 2
2x = 16
x = 8
- Finding y:
Substitute x back into the equation for y:
y = 14 - 8 = 6
Identifying the Digits
Thus, the digits of the two-digit number are:
- Tens digit (x) = 8
- Units digit (y) = 6
Finding the Product
Now, we calculate the product of the two digits:
- Product = x * y = 8 * 6 = 48
Conclusion
Therefore, the product of the two digits of the two-digit number is 48, confirming that the correct answer is option 'B'.
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The sum of the digits of two-digit number is 14 and the difference between the two digits number is 2. What is the product of the two digits of the two-digit number ?a)56b)48c)45d)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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