Multiple choice general knowledge math & puzzles

Kamla fasted on 1st, 3rd, 6th, 10th, 15th...... day of the year 2010 and she continued fasting in this pattern thereafter. Bimla fasted on 1st, 4th, 8th, 13th, 19th..... day of the year 2010 and maintained the pattern thereafter. When would they fast together again?

  1. 23rd December, 2010

  2. 13th September, 2010

  3. 21st December, 2010

  4. Never
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kamla's pattern: differences are 2, 3, 4, 5... so day n = 1 + 2+3+...+(n-1) = 1 + (n-1)n/2. Bimla's pattern: differences are 3, 4, 5, 6... so day n = 1 + 3+4+...+(n+1) = 1 + (n+2)(n-1). They fast together when 1 + (n-1)n/2 = 1 + (n+2)(n-1). This gives (n-1)n/2 = (n+2)(n-1), so n/2 = n+2, which gives n = -4, impossible for positive n. They never fast on the same day.

AI explanation

To find out when Kamla and Bimla would fast together again, we need to determine if there is a common day when both of their fasting patterns align.

Let's analyze their fasting patterns:

Kamla fasts on the 1st, 3rd, 6th, 10th, 15th... day of the year 2010. Bimla fasts on the 1st, 4th, 8th, 13th, 19th... day of the year 2010.

We can observe that both Kamla and Bimla fast on the 1st day of the year. However, after that, their fasting patterns do not align. Kamla fasts on the 3rd day, while Bimla fasts on the 4th day. The pattern continues in a similar manner where they fast on different days.

Therefore, there is no common day when both Kamla and Bimla would fast together again. Hence, the correct answer is option D - Never.

Keep practicing — related questions