A fruit seller had 60 kg of pears which he graded into 3 sizes A, B and C. The ratio of the mass of Grade A pears to the mass of Grade B pears to the mass of Grade C pears was 2 : 5 : 3. There were 7 Grade B pears per kilogram. This was 2 pears more than in one kilogram of Grade A pears and 3 pears less than in one kilogram of Grade C pears. What was the ratio of the number of Grade A pears to the number of Grade B pears to the number of Grade C pears?
The masses obey 2:5:3 = 12:30:18
So there are 12kg of A, 30kg of B, 18kg of C.
So if there were a,b,c of each type, and since
#pears = 1/density (where density = mass per pear)
1/b = 7
1/b = 1/a + 2
1/b = 1/c - 3
solve and you get 1/a = 5 and 1/c = 10
So a:b:c = 5:7:10