@cse23. I disagree with you.
When they have asked only for read, it means that the probablity of read operations is 1.
So, only for read operations, effective read time
= (hit ratio for cache)(cache access time) + (cache miss ratio)(Cache time + M.M time)
= 0.9 * 100 + (1 - 0.9)(100 + 1000)
SImilarly, only for write, effective write time = 1000 ns( because its the write through cache and largest of the cache time and M.M time is considered).
Now, effective access time(considering a mix of read and write)
= (probablity of read operations)* (effective read operation time)
+ (probablity of write operations)* (effective write operation time)
= 0.8 * 200 + 0.2 * 1000
= 360 ns