# 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 2nd 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