In a school with 400 students, the average of the age of the boys is 16 years and that of the girls is 12 years. If the average age of the school is 14 years 9 months. Then the number of girls in the school is.

Let the average age of Boys be ‘x’ According to question, x × 16 + (400 - x) × 12 = 400 × 14(3/4) 16x + 4800 - 12x = 400 × 59/4 4x + 4800 = 5900 4x = 1100 x = 275 Number of girls = 400 - 275 = 125 Alternate Method: By Alligation, Boys                       Girls 16                            12              59/4 59/4 - 12          :      16 - (59/4) 11/4                 :           5/4 11                    :           5 So Number of girls = 5/(5+11) of 400 = 5/16 of 400 = 125