Average of four numbers is 215. The ratio of first to second number is 4:7, the ratio of second to third number is 9:8 and the ratio of fourth to third number is 15:14. Find the average of the first and the fourth number.

Sum of all the four numbers = 215 × 4 = 860 Ratio of second and third number is 9:8 Ratio of fourth and third number is 15:14 Make third common: Third in (9:8) has 8 parts Third in (15:14) has 14 parts LCM of 8 and 14 is 56, so take third = 56 parts Then second = (9/8)×56 = 63 parts And fourth = (15/14)×56 = 60 parts So, ratio of second, third and fourth number is 63:56:60 Also, ratio of first to second is 4:7 Make second common: Second = 63 parts corresponds to 7×9, so first = 4×9 = 36 parts So, ratio of all four numbers = 36:63:56:60 Let the four numbers be 36x, 63x, 56x and 60x respectively. According to question, 36x + 63x + 56x + 60x = 860 215x = 860 x = 4 Desired Average = (36x + 60x)/2 = 96x/2 = 48x = 48×4 = 192