If the total number of hours worked $N=13500$, and the number of employees is $n=450$, then the mean number of hours worked per employee is given by:
$$\mu = \frac{N}{n}=30\:\text{hours}$$
We are given that the standard deviation $\sigma = 7\:\text{hours}$, and therefore we have that the number of hours worked per employee is normally distributed $T \sim \mathcal{N}(30, 49)$. We want to find the following probability:
$$P(T\gt 37) = 1-P(T\leq 37) = 1-\Phi\left(\frac{37-30}{7}\right) = 0.158655$$
However, a "trick" way of doing this would be to remember that approximately $68\%$ of the normal distribution lies within $1\sigma$ deviation, and thus we have that:
$$P(T > \mu + \sigma)\approx 1-(50\%+34\%)=0.16$$
Your looking at the question innaccurately. Take it slowly and break it down.
In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category.
First take the first part
5% of the applicants were found ineligible
What does this tell you? It tells you that 5% were ineligible and 95% were eligible. Let x be the number of total applicants, and e be the number of eligible candidates. We would get the following formula
x = (5/95) e + e
Now we look at the next line
85% of the eligible candidates belonged to the general category.
This is saying 85% of e (not x) belong to the general category. So letting n be the number of people not in the general category we would get
e = n + (85/15)n
e = n * 20/3
We are then given n
If 4275 eligible candidates belonged to other categories
So we have
n = 4275
Thus we have
e = 4275 * 20/3
e = 28500
And plugging this into our previous equation we get
x = 28500 + (5/95) * 28500
x = 30000
Hope that helps a little more.
Edit
Where does 85/15 come from?
Let e = eligible, n = non-generally eligible, and g = generally eligible. So we have
e = n + g
What we are trying to do is convert g to n since we don't know what g is. We do know that:
n = 0.15e
g = 0.85e
Thus we get that
n/0.15 = e
g = (0.85) * (n/0.15)
g = (0.85/0.15) n
g = (85/15) n
And that's where we get the 85/15. Basically think of it as "how much bigger is g than n?". If n is 15% of e and g is 85% of e then g is (85/15) times bigger than n so we get (85/15)n = g.
2nd edit
Why can't we convert (5/95) to (5/100)x?
Because of the following:
x = (5/95) e + e
x = (5/95) e + (95/95) e
x = (100/95) e
e = (95/100) x
You can put it all into one nice equation, but you can't just flop things around without going line by line to see what everything does.
Best Answer
It's Simple
For a $7 \times 7$ $(3\cdot2+1)$ board..there are $9$ $(3\cdot3)$ black squares
Similarly for a $13\times13$ $(6\cdot2+1)$ board..there will be $36$ $(6\cdot6)$ black squares
So white squares=$169-36=133$
Why $13$ ? Because $6\times6$ black squares means $6$ rows containing black squares and $7$ rows containing white squares ..
Similar case for columns...
So $13$ columns and $13$ rows