The sum of four numbers is 253. the ratio of the first to the second is 2 : 3. the ratio of the second to the third is 5 : 6. the ratio of the third to the fourth is 8 : 9. what is the average of the second and the third number?

From the problem statement we have, 
a+b+c+d=253 > 1
a/b=2/3 > 2
b/c=5/6 > 3
c/d=8/9 > 4

Substituting the value of a and d from statements 2 and 4 in 1 we get,
40b+51c=253*24 ---> 5

Substituting the vaue of b from statement 3 in statement 5 we get,
c=72, then b=60

Hence the average of 2nd and 3rd number will be 66

ANSWER: 66