A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added number, its digits are reversed. Find the number.
Answers
Given:-
- A two-digit number is 3 more than 4 times the sum of its digits.
- 18 is added number, its digits are reversed.
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To find:-
- The number.
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Solution:-
☆ Let, the original number in the form of 10x + y, where x is the digit in the tenth place and y in its unit place. When the digits are reversed the number will be in the form 10y + x.
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According to the question,
⇢ 10x + y = 3 + 4(x + y)
⇢ 10x + y = 3 + 4x + 4y
⇢ 10x - 4x = 3 + 4y - y
⇢ 6x = 3 + 3y
⇢ 6x - 3y = 3⠀⠀⠀⠀....[eq. 1]
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⇢ (10x + y) + 18 = (10y + x)
⇢ (10x + y) - (10y + x) = -18
⇢ 10x + y - 10y - x = -18
⇢ 9x - 9y = -18
⇢ 9(x - y) = -18
⇢ (x - y) = -18/9
⇢ (x - y) = -2⠀⠀⠀⠀....[eq. 2]
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⇢ x - y = -2
⇢ y = x + 2⠀⠀⠀ ⠀....[eq. 3]
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- On putting this value of equation 3 in equation 1 we get,
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⇢ 6x - 3y = 3
⇢ 6x - 3(x + 2) = 3
⇢ 6x -3x - 6 = 3
⇢ 3x - 6 = 3
⇢ 3x = 3 + 6
⇢ 3x = 9
⇢ x = 9/3
⇢ x = 3
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- Putting the value of x in equation 2
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⇢ x - y = -2
⇢ 3 - y = -2
⇢ y = 3 + 2
⇢ y = 5
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Therefore,
- 10 × 3 + 5 = 35
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Hence,
- The Original number is 35.
A N S W E R :
- The Original number is 35.
Given :
- A two-digit number is 3 more than 4 times the sum of its digit
- 18 is added number, its digits are reversed
To find :
- Find the Original number ?
Solution :
- Let ones place digit be x
- Tens place digit be y
- Original number = 10y + x
Number formed by reversing the digits = 10x + y
A two digit number is 3 more than 4 times the sum of its digit
According to the question,
=> 10y + x = 4(x + y) + 3
=> 10y + x - 4x - 4y = 3
=> 6y - 3x = 3
=> 2y - x = 1 (equation 1)
- Again, when 18 is added to the number then digits get interchanged
=> (10y - x) + 18 = 10x + y
=> 9x - 9y = 18
=> x - y = 2 (equation 2)
- On, adding equation (1) & (2)
=> 2y - x + (x - y) = 1 + 2
=> 2y - x + x - y = 3
=> Y = 3
- Substituting the values of y in equation (2)
=> x - y = 2
=> x - 3 = 2
=> x = 2 + 3
=> x = 5
Therefore,
- Number = 10y + x = 10 × 3 + 5 = 35
Hence,
- The Original number is 35.