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A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number.

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None of these

answer is C.

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Detailed Solution

Given a two-digit number.
Let the tens and the units digits in the number be x and y, respectively.
So, the number may be written as

10 x + y

.
According to the given condition.

10 x + y = 6 (x + y) + 3

\Rightarrow 4 x - 5 y = 3

........(1)
If we interchange the digits of original number then we get new number, that is,

10 y + x

According to the given condition.

10 y + x + 18 = 10 x + y

\Rightarrow 9 x - 9 y = 18

\Rightarrow x - y = 2

........(2)
Now multiplying equation (2) by

4

, we get,

4 x - 4 y = 8

.......(3)
On subtracting (3) from (1), we get,

4 x - 5 y - (4 x - 4 y) = 3 - 8

∴ y = 5

On substituting

y = 5

in (2), we get,

x - 5 = 2

\Rightarrow x = 7

∴

Number is

10 x + y = 10 (7) + 5 = 75

Therefore, option (3) is correct.

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