Question

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.​

Answer 1

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.

Answer 2

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.