Reim and Bindu are in a line with other students, waiting to see a movie. There are at most 30 students in the line. Reim says: “There are three times as many students after me in this line than before me.” Bindu says: “There are four times as many students after me in this line than before me.” How many students are in the line?
Let there be k students in front of Reim.
So there is k students in front + 3k students behind + Reim = 4k+1 students
Let N be the number of students in front of Bindu.
So there is N students in front + 4N students behind + Bindu = 5N+1 students
So the number of students is a product of both 4 and 5 + 1 more
20 is the only such product that is less than or equal to 30
So there are 21 students in the line.
Bindu is 5th and Reim is 6th.