The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits is 1 : 2?
8

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Solution

The correct option is A 8
Since the number is greater than the number obtained on interchanging the digits, so the tens digit is greater than the units digit.

Let tens and units digits be 2x and x respectively.

Therefore, the number is $(10 \times 2 x + x)$ and the number obtained on interchanging the digits is $(10 x + 2 x)$ .

Hence, the required equation is
$(10 \times 2 x + x) - (10 x + 2 x) = 36 9 x = 36 x = 4$

So, the units digit is 4 and the tens digit is $2 \times 4 = 8$ .

Thus, the number is 84.

The sum of the two digits is $(8 + 4) = 12$ and the difference between the digits is $8 - 4 = 4$ .

Then, the difference between the sum of the digits and difference of the digits is $(12 - 4) = 8$ .

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