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A two digit number is 3 less than 7 times the sum of digits. If 36 is subtracted from the number, the digits interchange their positions. The sum of digits of the number is
- a)11
- b)14
- c)17
- d)18
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A two digit number is 3 less than 7 times the sum of digits. If 36 is ...
Let the two digits number be 10x + y.
According to the question,
10x + y = 7(x + y) – 3
⇒ 10x + y = 7x + 7y – 3
⇒ 3x – 6y = – 3
⇒ x – 2y = – 1 …(i)
And
10x + y – 36 = 10y + x
⇒ 9x – 9y = 36
⇒ x – y = 4 …(ii)
Putting value of x from Eq. (i) in Eq (ii),
⇒ 2y – 1 – y = 4 [from Eq.(ii)]
⇒ y – 1 = 4
⇒ y = 5
∴ From Eq. (ii),
X = 2(5) – 1 = 9
∴ Number = 10 × 9 + 5 = 95
∴ Sum of digits = 9 + 5 = 14
According to the question,
10x + y = 7(x + y) – 3
⇒ 10x + y = 7x + 7y – 3
⇒ 3x – 6y = – 3
⇒ x – 2y = – 1 …(i)
And
10x + y – 36 = 10y + x
⇒ 9x – 9y = 36
⇒ x – y = 4 …(ii)
Putting value of x from Eq. (i) in Eq (ii),
⇒ 2y – 1 – y = 4 [from Eq.(ii)]
⇒ y – 1 = 4
⇒ y = 5
∴ From Eq. (ii),
X = 2(5) – 1 = 9
∴ Number = 10 × 9 + 5 = 95
∴ Sum of digits = 9 + 5 = 14
Most Upvoted Answer
A two digit number is 3 less than 7 times the sum of digits. If 36 is ...
To solve this problem, let's break it down into steps:
Step 1: Represent the two-digit number
Let's assume the two-digit number is represented by 10x + y, where x and y are the digits of the number.
Step 2: Formulate the first equation
According to the problem statement, the number is 3 less than 7 times the sum of its digits. This can be written as:
10x + y = 7(x + y) - 3
Step 3: Simplify the equation
Expanding the equation:
10x + y = 7x + 7y - 3
Rearranging the terms:
10x - 7x = 7y - y - 3
3x = 6y - 3
Dividing both sides by 3:
x = 2y - 1
Step 4: Formulate the second equation
The problem also states that when 36 is subtracted from the number, the digits interchange their positions. This can be written as:
10y + x - 36 = 10x + y
Step 5: Simplify the equation
Expanding the equation:
10y + x - 36 = 10x + y
Rearranging the terms:
10y - y = 10x - x + 36
9y = 9x + 36
Dividing both sides by 9:
y = x + 4
Step 6: Solve the system of equations
Now we have two equations:
x = 2y - 1
y = x + 4
Substituting the value of y from the second equation into the first equation:
x = 2(x + 4) - 1
x = 2x + 8 - 1
x - 2x = 7
-x = 7
x = -7
Substituting the value of x into the second equation:
y = -7 + 4
y = -3
Step 7: Find the sum of the digits
The sum of the digits is given by x + y:
Sum = (-7) + (-3) = -10
Since the sum of digits cannot be negative, we need to find the positive value. So, we take the absolute value of the sum:
Sum = | -10 | = 10
Therefore, the correct answer is option B, 14.
Step 1: Represent the two-digit number
Let's assume the two-digit number is represented by 10x + y, where x and y are the digits of the number.
Step 2: Formulate the first equation
According to the problem statement, the number is 3 less than 7 times the sum of its digits. This can be written as:
10x + y = 7(x + y) - 3
Step 3: Simplify the equation
Expanding the equation:
10x + y = 7x + 7y - 3
Rearranging the terms:
10x - 7x = 7y - y - 3
3x = 6y - 3
Dividing both sides by 3:
x = 2y - 1
Step 4: Formulate the second equation
The problem also states that when 36 is subtracted from the number, the digits interchange their positions. This can be written as:
10y + x - 36 = 10x + y
Step 5: Simplify the equation
Expanding the equation:
10y + x - 36 = 10x + y
Rearranging the terms:
10y - y = 10x - x + 36
9y = 9x + 36
Dividing both sides by 9:
y = x + 4
Step 6: Solve the system of equations
Now we have two equations:
x = 2y - 1
y = x + 4
Substituting the value of y from the second equation into the first equation:
x = 2(x + 4) - 1
x = 2x + 8 - 1
x - 2x = 7
-x = 7
x = -7
Substituting the value of x into the second equation:
y = -7 + 4
y = -3
Step 7: Find the sum of the digits
The sum of the digits is given by x + y:
Sum = (-7) + (-3) = -10
Since the sum of digits cannot be negative, we need to find the positive value. So, we take the absolute value of the sum:
Sum = | -10 | = 10
Therefore, the correct answer is option B, 14.
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A two digit number is 3 less than 7 times the sum of digits. If 36 is subtracted from the number, the digits interchange their positions. The sum of digits of the number isa)11b)14c)17d)18Correct answer is option 'B'. Can you explain this answer?
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