# The sum of a two-digit number lying between 10 and 60 and the number obtained by reversing the digits of that number is divisible both by 11 and 8. Th

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The sum of a two-digit number lying between 10 and 60 and the number obtained by reversing the digits of that number is divisible both by 11 and 8. The difference of the digits is 6. If the original number is divided by 11, the remainder is:
1. 6
2. 3
3. 5
4. 7

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Correct Answer - Option 1 : 6

Let;

The number is = xy = 10x + y

according to question;

10 < (10x + y) < 60

After reversing the digits of the number;

New Number = 10y + x

The new number is divisible by 11 and 8.

|x - y| = 6 ----(1)

Now the sum of number and New number = (10x + y) + (10y + x)

11(x + y)

The sum is divisible by 11 and 8.

So, x + y is divisible by 8

or x + y = 8 ----(2)

From equation (1) and (2)

2x = 14

x = 7 and y = 1

So, the number is 17 (lying between 10 and 60)

If we divide 17 by 11 the remainder is 6.

Hence, "6" is the correct answer.