The question is to find the time taken for,
$\frac{\Large100 \space \text{fetch operations and $60$ operand read operations and $40$ memory
operand write operations}}{\Large\text{total number of instructions}}$.
Total number of instructions $=100+60+40 =200$
Time taken for $100$ fetch operations(fetch = read) $= 100*((0.9*1)+(0.1*5))$
$1$ corresponds to time taken for read when there is cache hit $= 140 \,\text{ns}$
$0.9$ is cache hit rate
Time taken for $60$ read operations,
$= 60*((0.9*1)+(0.1*5))$
$= 84\,\text{ns}$
Time taken for $40$ write operations
$= 40*((0.9*2)+(0.1*10))$
$= 112\,\text{ns}$
Here, $2$ and $10$ are the times taken for write when there is cache hit and no cache hit respectively.
So,the total time taken for $200$ operations is,
$= 140+84+112$
$= 336\,\text{ns}$
Average time taken $=$ time taken per operation
$=\dfrac{336}{200}$
$= 1.68\,\text{ns}$