In a newly established memory organization, there are two level, L₁ memory is 5 times faster than L₂ and its execution time is 30 ns less than the average accessing time. L₁ access time is 30 ns. What is the hit ratio of L₁?
(A) 0.25
(B) 0.5
(C) 0.75
(D) None of these.


Answer: (C)

Explanation: Hit ratio of L₁ = H₁= ?
Hit ratio of L₂ = H₂ = 1 (hit ratio of highest level memory is always 1)
L₁ access time T₁ = 30 ns
It is 30 ns less than the average access time. So,

T1 = TAvg - 30 ns 
30 = TAvg - 30 
TAvg = 60ns 

Level 1 memory is 5 times faster than level 2. So,

T2 = 5T1
T2 = 5*30 
T2= 150 

Therefore,

TAvg = H1T1 + (1 - H1)*H2*(T2)
TAvg = H1(30) + (1 - H1)*1*(150)
60 = 30H1 +150 -150H1
120H1 = 150 - 60 
H1 = 90 / 120
H1 = 3 / 4
H1 = 0.75 

So, option (C) is correct.

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