IMAT 2020 Q5 [Tin of Sweets]

36% of the contents of a tin of sweets have been eaten. Today, 25% of the remaining sweets will be eaten. The same number of sweets will be eaten on each of the following 2 days.

What % of its original contents will it then contain?

A. 24
B. 25
C. 16
D. 9
E. 15

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

For simplicity, let’s say we originally start with 100 sweets in the tin. If we have 36% of 100 sweets eaten (100-36 = 64) , then 64 would be leftover. Now we need to take 25% of the remaining sweets, so we will need to take (64)(0.25) = (64)/(4) = 16. So if 25% of 64 sweets are taken, then we are left with 64-16 = 48 left. Note that it says the same NUMBER are taken the next two days, not PERCENT, so we are using 16 sweets instead of 25% of the remaining total.

Over the next two days: 48-16-16 = 48 - 32 = 16

So we are left with 16 sweets. But wait, didn’t we want to find the percentage of how many were left from the original day? We just need to say 16%, because we started with 100 sweets which were to represent 100%.

Using calculation tricks like this, albeit simple, can really help simplify the problem and make it much easier to do mentally. What do you prefer? Taking 25% of 64% or taking 25% aka ¼ of 64 candies. Perspective is everything.

\fcolorbox{red}{grey!30}{Therefore the answer is C, $16$%}