Question

Unmesh is facing Jayesh and when he hears a bell ring he turns towards Rajesh by making 90 shift. He continues to do this every time the bell rings. If the bell rang 3926 times, whom will Unmesh be facing?

• A. Rajesh
• B. Mahesh
• C. Suresh
• D. layesh

Answer 1

The Correct Option is B

To determine whom Unmesh will be facing after the bell rings 3926 times, we need to understand the sequence of 90-degree turns he makes. If Unmesh starts facing Jayesh and turns 90 degrees each time the bell rings, Unmesh's position after each turn will be as follows:

1. Starting facing Jayesh

2. One bell ring (90-degree turn): Faces Rajesh

3. Two bell rings (180-degree total turn): Faces Mahesh

4. Three bell rings (270-degree total turn): Faces Suresh

5. Four bell rings (360-degree full circle): Back to facing Jayesh

The pattern repeats every four rings. To find whom Unmesh faces after 3926 rings, we calculate the remainder of 3926 divided by 4, as it determines his final position in the sequence.

Calculating 3926 % 4:

3926 divided by 4 equals 981 with a remainder of 2.

Since the remainder is 2, Unmesh will be facing Mahesh after the 3926th bell ring.

Answer 2

Each bell ring turns Unmesh through a quarter turn, so his facing direction repeats in a cycle of four: after every four rings he is back to facing the same person he started with, in this case Jayesh. This means only the remainder left over after dividing the total number of rings by four actually decides who he ends up facing, the completed groups of four rings cancel out entirely.

Dividing 3926 by 4 gives 981 complete groups of four, using up \( 981 \times 4 = 3924 \) rings, with \( 3926 - 3924 = 2 \) rings left over.

So the final two rings of the 3926 decide the answer, starting fresh from facing Jayesh: the first of these two rings turns him to face Rajesh, and the second turns him to face Mahesh.

1. Option A (Rajesh): This is where Unmesh would be after only one leftover ring, not two, so this is incorrect.
2. Option B (Mahesh): This matches exactly where two leftover rings, after all complete cycles of four are removed, leave Unmesh facing, so this is correct.
3. Option C (Suresh): This would be his position after three leftover rings, not two, so this is incorrect.
4. Option D (layesh, Jayesh): This would only be correct if the leftover were zero or a full four rings, not two, so this is incorrect.

With a remainder of exactly two rings after removing all complete four-ring cycles, Unmesh ends up facing Mahesh.

the correct answer is Option B: Mahesh.