Question

The average of 8 numbers is 20. The average of first two numbers is 1 21 3 and that of next three is 1 15 2 . If the sixth number is less than the seventh and the eighth numbers by 4 and 7 respectively, than the eighth number is-

Answer 1

Answer:

i) Let the 8 numbers in the order be a, b, c, d, e, f, g & h  

ii) Since their ave. is 20, their sum: a + b + c + d + e + f + g + h = 8*20 = 160 ---- (1)  

iii) a + b = 31 ------ (2) [Since average of firs two = 15 and 1/2]  

Similarly c + d + e = 64 ----- (3) [Since their average = 21 and 1/3]  

iv) Subtracting the sum of (2) & (3) from (1), f + g + h = 65 ------- (4)  

v) From the other given data, f = h - 7 ------ (5) and f = g - 3 ------ (6)  

So from (5) & (6): g - 3 = h - 7  

==> g = h - 4 ------ (7)  

Replacing f = h - 7 and g = h - 4 in (4),  

h - 7 + h - 4 + h = 64  

Solving h = 25  

Thus 8th number is 25