sixpointer wrote:17. A man starts a piece of work . Starting from the second day
onwards everyday new man joins .With every new man joining the
work that each man can do per day doubles .The work is completed in 5
days .On which day would they have completed the work ,if the work
that each of them could do per day had remained constant.?
1.10th 2.12th 3. 15th 4. 18th 5.16th
Let's say that on day 1, the man does x work.
On day 2, there are 2 men, each of whom do 2x work. So, 4x work gets done.
On day 3, there are 3 men, each of whom do 4x work. So, 12x work gets done.
On day 4, there are 4 men, each of whom do 8x work. So, 32x work gets done.
Finally, on day 5, there are 5 men, each of whom do 16x work. So, 80x work gets done.
Total: x + 4x + 12x + 32x + 80x = 129x work.
If the work remains constant, then the progression is:
x + 2x + 3x + 4x + 5x + .... + nx, on which n is the last day. We need that series to sum to 129.
Since we have a series of consecutive numbers, we could use the formula:
sum = # of terms * average of terms
but that's going to be some ugly math:
sum = n * (first term + last term)/2
129 = n * (1 + n)
129 = n + n^2
0 = n^2 + n - 129... some ugly quadratic!
So, rather than actually do all that ugly math, it's much quicker to backsolve at this point:
Starting with B or D, I'd choose D since it seems like we need a big number.
If n=18, then our sum is:
sum = 18 * (1+18)/2
sum = 18 * 9.5
sum = way too much!
Try B:
if n = 12, then we have:
sum = 12 * (1 + 12)/2
sum = 12 * 6.5
sum = way too small!
Accordingly, the answer has to be (C) 15.
