let A: x+10 hrs.....1 work = 1 hr........1/(x+10)work
B: x hrs................1 work= 1 hr........1/(x)work
now we r given a relation: B=10%A+A
1/(x)=10%(1/(x+10))+1/(x+10)
x=100
A:1hr.......1/110 work
660 sprocket: 660/110=6
Ans: A

My explanation:


*** A ***
work = 660
hours = b + 10
rate = a

work = rate * time
(1) 660 = (b+10)a

*** B ***
work = 660
hours = b
rate = 1.1a

work = rate * time
(2) 660 = 1.1ab

*** solve eqs 1 & 2 for a ***
(1) 660 = (b+10)a
(2) 660 = 1.1ab

(b+10)a = 1.1ab (div both sides by a, I can't solve a at this point so far)
b + 10 = 1.1b
b = 100

Recall *** A and do work/time***
work = 660
hours = b + 10
rate = a

660/110 = 6