Subtraction by Addition in time computations

Janice watches a film. It finishes at 8.12 pm. The film is 2 hours 36 minutes long. At what time did it start?             

1. 4.24 pm
2. 5.36 pm
3. 5.46 pm
4. 5.48 pm
5. 5.54 pm

This is a question given in the primary levels (primary A and B) of the 2^nd International Vedic Mathematics Olympiad (IVMO 2022).

Of course, this problem can be solved using the method taught in the primary grades, but it will involve several regroupings:

                         8: 1 2

– 2: 3 6

I can imagine my Grade 3 teacher explaining thus:

“2 minus 6, cannot be, borrow one from one; 12 minus 6 is 6.              

                         8: 0¹2

– 2: 3 6

                                6

“0 minus 3, cannot be, borrow one from 8. Since you are borrowing from 1 hour, which has only 60 minutes, you will only have 6 in the minuend, not 10. So we have 6 minus 3 equals 3.”

                         7: 6¹2

– 2: 3 6

                            3 6

“finally you will have 7 minus 2 equals 5.”  

  7: 6¹2

– 2: 3 6

                        5: 3 6

The movie started at 5: 36 PM.

An easier way to solve this problem is by using the technique which we call subtraction by addition. (See Chapter 3 – Subtraction without borrowing of our book, 25 Math Short Cuts).

Imagine the movie to be 24 minutes longer: it is 2:36 + 24 = 3:00 hours long.

So it will finish 24 minutes later or at 8:12 Pm + 24 minutes = 8:36 PM. The we can easily determine the starting time:

               8: 12 + 24 minutes = 8: 3 6 PM

               2: 36 + 24 minutes = 3: 0 0

                                                 5: 3 6 PM