Question

Given that 45 is the difference between a number and that formed by reversing it's digits. If the sum of the digits of the number is 13,then find the number. explain with full solution​

Answer 1

Answer:

Step-by-step explanation:

Difference between the Original Number and the Reversed Number = 45

Sum of the digits of the number = 13

Original Number -

• Let the Units Place be x

• Tens Place be 10(13 - x)

The Original Number =

10(13 - x) + x

130 - 10x + x

130 - 9x . ..[ 1 ]

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Number with Reversed Digits -

• Units Place will be (13 - x)

• Tens place 10(x)

Number with Reversed Digits =

10x + (13 - x)

10x - x + 13

9x + 13 . .[ 2 ]

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According to the Question ;

Difference between the Original Number and Reversed Number is 45.

130 - 9x - (9x+13) = 45

130 - 9x - 9x - 13 = 45

130 - 18x - 13 = 45

117 - 18x = 45

-18x = 45 - 117

-18x = --72

18x = 72

x = 72/18

x= 4

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Value of 10(13 - x) =

10(13-4)

130 - 40

= 90

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The Number =

90+4

= 94

The Original Number is 94.

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VERIFICATION =

By Reversing the Digits of 94 the Number is 49. If their difference is 45, then the answer is Correct.

94 - 49 = 45

45 = 45

The Original Number is 94.