The question goes like this:
On Tuesday, a watchmaker made 4 more watches than he made during the previous day. If he made 16% more watches on Tuesday than on Monday, how many watches did he make on Tuesday?
a) 20 b) 21 c) 25 d) 29
The way I'm thinking, there are 2 ways to solve this problem.
Approach 1:
The first is that we create expressions. Let x be the number of watches made on monday. Watches made on Tuesday are 4 more than those made on Monday, so the expressions for watches made on tuesday = x + 4. Moreover, they were also 16% more than those made on monday. So another expression for watches made on tuesday = x + (16/100)*x = 1.16x. We equate 1.16x to x+4 and find that c) 25 is the correct answer.
Approach 2:
Another method to do this is to plug in the answer choices. Lets start with a. If watches made on tuesday are 20, those made on Monday must be 20-4 = 16. % increase here is (4/16) * 100 = 25%. But our % increase was 16% so it is wrong. Lets check c)25 now. 25-4 is 21 which gives a % increase = (4/21)*100 = 19% which is also incorrect. By this approach, d) 29 gives the correct answer i.e. 16% so it much be a correct solution.
My question here is, which of these is the correct answer, C)25 or D)29? The book I'm following uses the 2nd approach I mentioned and says that D) is the correct answer. However, I can't seem to find the flaw in the logic used in Approach 1.
Both approaches are correct, but you failed to do one final step in the first approach. You found $x$ as the number of watches produced on Monday, but the question asked for Tuesday, so you need to add 4 to 25, which gives the correct answer of 29 watches.
In short: be more careful!