The average of 16 numbers is 48. The average of the first seven numbers is 45 and the average of the next 6 numbers is 52. If 14th number is 11 less than 15th number and 5 more than 16th number , Then the average of 15th and 16th numbers is ?
D
Correct answer
Explanation
Total sum of 16 numbers = 16 × 48 = 768. Sum of first 7 numbers = 7 × 45 = 315. Sum of next 6 numbers = 6 × 52 = 312. So sum of 14th, 15th, and 16th numbers = 768 - 315 - 312 = 141. Given: a14 = a15 - 11 and a14 = a16 + 5. So a16 = a14 - 5 = a15 - 16. Then a14 + a15 + a16 = (a15 - 11) + a15 + (a15 - 16) = 3a15 - 27 = 141, giving a15 = 56. Then a16 = 56 - 16 = 40. Average of 15th and 16th = (56 + 40) / 2 = 48.