Question

The sum of the digits of a two-digit number is 10.The number formed by reversing the digits is 18 less han the original number. Find the orginal number
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Answer 1

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Answer 2

It is given that,

• The sum of the digits of a 2 - digit no. = 10
• The number formed by reversing the digits is 10 less than the original number.

Let the unit digit be ' x ' and tens digit be ' y ' of the 2 - digit number.

According to first case,

i ) x + y = 10

From this equation, we can find the value of x.

➡ x = 10 - y _______________ ( ! )

Now,

According to second case,

ii ) 10x + y + 18 = 10y + x

➡ 10x - x + y - 10y = - 18

➡ 9x - 9y = - 18

➡ 9 ( x - y ) = -18

➡ x - y = - 18/9

[ Substitute the value of ' x ' given in eq. ( ! ) ]

We get,

➡ 10 - y - y = - 2

➡ 10 - 2y = -2

➡ -2y = -2 - 10

➡ -2y = - 12

➡ y = -12/-2

•°• y = 6

Now,

Substitute the value of ' y ' in eq. ( ! ) in order to find the value of ' x '.

We get,

x = 10 - 6

•°• x = 4

Original Number :

10y + 6

=> 10 × 6 + 4

➡ 60 + 4

➡ 64

Hence,

The original number is 64.

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