Question

Xsum of 2 digit number & the numerator obtained by reversing the digits is 154 .if the digit differ by 4

Answer 1

Correct Question :

The sum of 2 digits number & the number obtained by reversing the digits is 154 .If the digit differ by 4. Find the Original Number.

AnswEr :

Let the Unit Digit be x and, Ten's Digit be y

• Original No. = (10y + x)
• Reversed No. = (10x + y)

Let the Greater Number be x

Then, Digits Differ by 4

↠ Greater No. - Smaller No. = 4

↠ x - y = 4

↠ x = 4 + y ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq.( I )

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• According to the Question Now :

⇒ Original No. + Reversed No. = 154

⇒ (10y + x) + (10x + y) = 154

⇒ 11y + 11x = 154

⇒ 11(y + x) = 154

• Dividing both term by 11

⇒ (y + x) = 14

• putting the value of x from eq.( I )

⇒ (y + 4 + y) = 14

⇒ 2y + 4 = 14

⇒ 2y = 14 - 4

⇒ 2y = 10

• Dividing both term by 2

⇒ y = 5

• Putting the value of y in eq.( I ) :

↦ x = 4 + y

↦ x = 4 + 5

↦ x = 9

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• O R I G I N A L ⠀N U M B E R :

◗ (10y + x)

◗ 10(5) + 9

◗ 50 + 9

◗ 59

∴ Therefore, Original Number is 59.

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• V E R I F I C A T I O N :

⇒ Original No. + Reversed No. = 154

⇒ (10y + x) + (10x + y) = 154

⇒ [ 10(5) + 9 ] + [ 10(9) + 5 ] = 154

⇒ [ 50 + 9 ] + [ 90 + 5 ] = 154

⇒ 59 + 95 = 154

⇒ 154 = 154 ⠀⠀⠀⠀⠀⠀Hence, Verified!

#answerwithquality #BAL

Answer 2

Answer:

10x+y+10+y=154

11x+11y=154

x+y=14

x-y=4

2x=18

x=9

y=5

The number is either 95 or 59.