What digit will come in the place of 'a' in the number 1a5a01, if it is divisible by 11?

Correct option is D

Given:

The number is 1a5a01 and it must be divisible by 11.

Concept Used:

A number is divisible by 11 if the difference between the sum of its digits at odd positions and the sum of its digits at even positions is either 0 or divisible by 11.

Solution:

Let us take the digits of the number 1a5a01 at odd and even positions.

Odd positions: 1, 5, 0

Even positions: a, a, 1

The sum of digits at odd positions is:

1 + 5 + 0 = 6

The sum of digits at even positions is:

a + a + 1 = 2a + 1

According to the divisibility rule of 11:

6 - (2a + 1) = 5 - 2a

For the number to be divisible by 11, 5 - 2a must be divisible by 11.

Try different values of a to satisfy the condition.

If a = 3, 5 - 2(3) = 5 - 6 = -1, which is not divisible by 11.

If a = 4, 5 - 2(4) = 5 - 8 = -3, which is not divisible by 11.

If a = 8, 5 - 2(8) = 5 - 16 = -11, which is divisible by 11.

Therefore, the digit that comes in place of a is 8.