The average of 20 numbers is 80. The average of first 10 numbers is 76.5 and that of next 7 numbers is 82. The 18th number is 3 more than the 19th number but 3 less than the 20th number. What is the average of 18th and 19th numbers?
Answer & explanation
Correct answer: option 4
Sum of 20 numbers = 20 × 80 = 1600
Sum of first 10 numbers = 10 × 76.5 = 765
Sum of next 7 numbers = 7 × 82 = 574
Sum of last 3 numbers = 1600 - ( 765 + 574) = 1600 - 1339 = 261
ATQ,
Let 18th number = a
19th number = a - 3
20 th number = a + 3
Now , a + a - 3 + a + 3 = 261
3a = 261
a = 87
Average of 18th & 19th number = \(\frac{87 + ( 87 - 3 ) }{2}\) = 85.5