4. Squirrel Pusistik and Lohmatik ate a basket of berries and a bag of seeds, which contained more than 50 but less than 65 seeds, starting and finishing at the same time. At first, Pusistik ate berries, and Lohmatik ate seeds, then (at some point) they switched. Lohmatik ate berries six times faster than Pusistik, and seeds only three times faster. How many seeds did Lohmatik eat if Lohmatik ate twice as many berries as Pusistik?
Problem 826
Official solution
# Answer: 54.
Solution. Divide the berries into 3 equal parts. Each part, Lomhatic ate 6 times faster than Pushistik, but there are two parts, so he spent only 3 times less time on the berries than Pushistik. Therefore, Pushistik ate the seeds in one-third the time of Lomhatic. Since Pushistik eats three times slower, he ate 9 times fewer seeds than Lomhatic. Dividing the seeds in the ratio of 9:1, we see that Pushistik got one-tenth of the seeds, from which it is not difficult to understand that there were 60 seeds in the bag. Therefore, Pushistik ate 6 seeds, and Lomhatic - 54.
Comment. Correct solution - 20 points. Solution started, with some progress - 5 points. Solution started, but no significant progress - 1 point. Incorrect or no solution - 0 points.