let total students =100
solicited = 40% ; 40 students contributed 400$ each
40*400 = .6x
x= 26,666 $
26,666*40% = $ 10666
10666 per 60 students = 10666/60 ; ~ 177 $
IMO B

Let the total amount required be $T and the total number of contributors be 10. So $ 400*4=$1600 has already been received from 4 contributors which is equal to 60% or 3/5th of T. The remaining $2/5*T is equal to 1600*(5/3)*(2/5)=$(3200/3) has to be collected from the remaining 6 contributors.
Therefore average contribution required = (3200)/(3*6)=177.777=$177.78. Ans: B

Algebric Approach:

Let Total Fund =F
Total Solicitors = S
Fund already collected = 0.6F, So remaining fund to be collected = 1-0.6F= 0.4F
Solicitors already contributed = 0.4S. Remaining solicitors to donate = 1- 0.4S = 0.6S
We need to calculate average donation by remaining solicitors, i.e., 0.4F/0.6S = (2/3)(F/S)
We have, 0.4S*400 = 0.6F
=> F/S = 800/3
So, Avg. contribution = (2/3)(F/S) =(2/3)(800/3) = $177.78 [Ans. B]
_________________

Consider that school need's 100 $ and there are total 10 Men for donation
Now, they have already received 60$ from 40% of men i.e 60$ from 4 men = 60 / 4 = 15 viz equivalent to 400 $ per person in original question
Now for remaining 40$ we have 6 Men for donation =40/6 = 6.66
Therefore , if 15 is equivalent to 400$ , then 6.66 is equivalent to how much?
(15/6.66)=(400/X)
X turn's out to be 177.6

Please do let me know if this help's

Let T = the total number of people who will be solicited.
Let B = the total amount required for the new building.

A school has received 60% of the amount it needs for a new building by receiving a donation of $400 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations.
In other words: (# of donators)($400 per donor) = 60% of amount needed for building.
Substitute to get: (40% of T)($400) = 60% of B
In other words: (0.4T)(400) = 0.6B

How much average contribution is required from the remaining targeted people to complete the fund raising exercise?
Let C = the required contribution from each remaining person (who hasn't yet donated).
60% of the people have not yet been solicited
They still need to raise the remaining 40% of the total cost of the building
We can write: (# of remaining donators)(C) = 40% of amount needed.
Substitute to get: (60% of T)(C) = 40% of B
In other words: (0.6T)(C) = 0.4B
Solve for C to get: C = (0.4B)/(0.6T) = 4B/6T = (2/3)(B/T)

As we can see, to find the value of C, we need the value of B/T
To do so, we can use the fact that (0.4T)(400) = 0.6B
Divide both sides by 0.4T to get: 400 = 0.6B/0.4T
Multiply numerator and denominator by 10 to get: 400 = 6B/4T
Simplify to get: 400 = 3B/2T
Multiply both sides by 2 to get: 800 = 3B/T
Divide both sides by 3 to get: 800/3 = B/T

Now take C = (2/3)(B/T)
And substitute to get: C = (2/3)(800/3)
Simplify: C = 1600/9 ≈ $177

Answer: B
_________________

Assume the total number of people from whom the school will solicit donations is 100
that means 40 have paid $400 => 16000 represents 60% of the total amount X

x= 16000/0.6
remaining contribution = 16000/0.6 - 16000 = 64000/6
60 people need to contribute this amount,
hence on an average one person has to contribute =64000/[6*60] = $177.78