A cricket coaching camp runs two batches. Batch A has 24 players with mean age 15 years, and Batch B has mean age 12 years. When the two batches train together the mean age of all the players is 14 years. How many players are in Batch B?

Let Batch $B$ hold $n$ players. The two batches together contribute $24\times 15+12n$ years of age to $24+n$ players, so $(360+12n)/(24+n)=14$, giving $360+12n=336+14n$ and therefore $2n=24,n=12$. Check: $(360+144)÷36=504÷36=14$. The combined mean 14 sits 1 year from Batch A's mean and 2 years from Batch B's, and a group's SIZE is proportional to the OTHER group's distance, so A : $B=2$ : 1 and $B=12$; pairing each batch with its own distance reverses the ratio and gives 48. The value 24 assumes the batches are the same size, which would put the combined mean midway at 13.5, and 36 is the total number of players in the two batches together.