Batch X has 20 more students than Batch Y. Batch X averages 55 marks and Batch Y averages 70 marks. The two batches together average 61 marks. How many students are in Batch Y?

Explanation

1. 01

   Let Batch Y have n students, so Batch X has $n + 20$.

2. 02

   $55(n + 20) + 70n = 61(2n + 20)$.

3. 03

   $125n + 1{,}100 = 122n + 1{,}220$, so $3n = 120$ and $n = 40$.