# 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?**** **

**4.24 pm****5.36 pm****5.46 pm****5.48 pm****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: 0^{1}2

– 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: 6^{1}2

– 2: 3 6

3 6

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

7: 6^{1}2

– 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**