Although this question is one on Word problems, it also has strong undercurrents of Ratio concepts based on which you need to solve this question. Instead of solving it the usual way of dividing the total of 8 sandwiches among 3 people and dealing with fractions, I’d like to take an approach where I can use integer values and the concept of money- because both these concepts can be easily understood and it will make you more confident with such questions.
The total number of sandwiches is 8; we need to divide this among 3 persons. It’s very clear that this involves uneven division by 3. So, to make it simple, let us take the cost of one sandwich to be $3.
This means that the total value of the 8 sandwiches is $24, of which $15 was contributed by P and $9 was contributed by Q.
R did not contribute anything but still ended up getting an equal share. What does this mean?
It means that he got an equal share of the total value $24 which comes to $8.
This also means that the other two persons
P and Q saw their respective shares being reduced to $8 since they were magnanimous enough to
share their sandwiches with R.
Q’s share was 9 and it went down to 8. This means, he should have given $1 to R (or in other words, \(\frac{1}{3}\)rd of a sandwich to R).
P’s share was 15 and it went down to 8. This means, he should have given $7 to R (or in other words, \(\frac{7}{3}\)rd of a sandwich to R).
See how the sum of 7/3 and 1/3 gives you 8/3 which is the value you would have obtained even if you took the traditional approach of dividing 8 by 3.
Since R paid $8 to P and Q and the money needs to be split in the ratio of the sandwiches they shared with R, it only means that P got $7 and Q got $1.
The correct answer option is E.
A point to note is that it’s wrong to assume that the money given by R to P and Q was divided uniformly among them. Do not make this mistake, or option B is waiting for you.
Hope that helps!
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