Question:hard

The regular mathematics faculty could not teach because of being sick. As a stop-gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am, with a maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic, so the classes started at different times on different days.

Mr. Singh did not teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he did not teach probability. The class on Monday started at 7:00 am, but Mr. Singh did not teach it. Mr. Dutta did not teach ratio and proportion. Mr. Banerjee, who did not teach set theory, taught a class that started five minutes later than the class in which probability was taught. The teacher in Friday's class taught set theory. Wednesday's class did not start at 7:10 am. No two classes started at the same time.

78. The option which gives the correct teacher-subject combination is:

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Work out which day Mr. Singh teaches first (it has to be Friday), then use the clue that Friday's teacher taught set theory to fix his subject directly.
Updated On: Jul 10, 2026
  • Mr. Chatterjee - ratio and proportion
  • Mr. Banerjee - calculus
  • Mr. Chatterjee - set theory
  • Mr. Singh - set theory
Show Solution

The Correct Option is D

Solution and Explanation

Instead of deriving the whole week fresh, this method walks through the four given teacher-topic pairs one at a time and tests each against the clues.

  1. Mr. Chatterjee - ratio and proportion: Mr. Chatterjee's only stated day is Wednesday, and once Mr. Dutta is fixed to probability and Mr. Singh to set theory (from the Friday clue), the calculus-at-7:20-am clue can only be satisfied by Mr. Chatterjee, because Mr. Banerjee's class works out to 7:05 am. So Mr. Chatterjee taught calculus, not ratio and proportion. This option is wrong.
  2. Mr. Banerjee - calculus: Mr. Banerjee's start time is always five minutes after the probability class. Since the probability class (Mr. Dutta, Monday) starts at 7:00 am, Mr. Banerjee's class starts at 7:05 am, not 7:20 am, so he cannot be the calculus teacher. This option is wrong.
  3. Mr. Chatterjee - set theory: Friday's teacher taught set theory, and Mr. Chatterjee teaches on Wednesday, not Friday, so set theory is not his topic. This option is wrong.
  4. Mr. Singh - set theory: Mr. Singh cannot teach Monday or Thursday, and Wednesday belongs to Mr. Chatterjee, so he is on Friday, and Friday's teacher taught set theory. This option matches every clue.

The correct combination is Mr. Singh, set theory, because he is the only teacher whose day (Friday) is directly tied to the set theory topic by the puzzle's own wording.

Let's summarize:

  • Working out each teacher's day first (Chatterjee-Wednesday, Singh-Friday, Dutta-Monday, Banerjee-Thursday) pins down every topic through the calculus-timing and set-theory-on-Friday clues.
  • Three of the four listed pairs break a stated clue; only Mr. Singh with set theory survives all of them.

So the teacher-subject combination that is actually correct is Mr. Singh - set theory.

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