'x' number of men can finish a piece of work in 30 days.If there were 6 men more, the work could be finished in 10 days less. The original number of men is?
A. 6
B. 10
C. 12
D. 15
Solution(By Examveda Team)
x men can finish a work in 30 days. It menas they need (x *30) men -days to complete the work.
If there were 6 men more, then
No. of men now = (x +6)
They can finish the work in (30 -10) days = 20 days.
They need [(x+6) *20] men days to complete the work.
In the both case they are finishing the same work. That is
Work in first case = Work in second case
Thus,
x * 30 = (x +6) *20
30x = 20x + 120
10x = 120
x = 12 men.
Original number of men = 12
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Very nice solution
thanks examveda..
If we do this question by option checkiing ..
then..
A) let x=6
total work must be remain the same
6*30=180
after increasing 6 men
(6+6)*(30-10)=240
180 nnot equal to 240
B)10*30=300
(10+6)*(30-10)=320
c)12*30=360
(12+6)*(30-10)=360
therefore C is correct
Thanks TEAM EXAMVEDA........
Here, my Method is Men one days work is 1/30-----(1)
whereas Men one days work is 1/20------(2)
Now subtracting (2)-(1) i.e.
X+6 men one days work - X men one Days work= 1/20-1/30;
X+6-x= 1/20-1/30... i.e.,
6 men one days work is 1/60...
Now from this one man one days work is 1/360.
now From initial statement 1 X men finish a piece of work in 30 days...
so (1/360)*X*30=1
by solving this we will get X = 12;
So initially 12 men present...
I think both methods are good. However, Through work equivalence it could be done in one line:
x*30 = (x +6)*20 x= 12 men.
Good explanation @Leelanand.