SravnaTestPrep
A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
A. 1/3
B. 2/9
C. 9/49
D. 7/19
E. 1/6
Quote:
To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/3rd the time that C would take to complete the task alone
A=A
B=2A
B=\(\frac{2}{3}\)C
Put the value of B here, so that we can get everything in term A
so, C=3A
Quote:
B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked
A=x
B=\(\frac{1}{2}\)x
B=\(\frac{3}{2}\)C
In this also we put value of B so that we can get everything in term of x
C=\(\frac{1}{3}\)x
Now for suppose the x=6.
A=6
B=3
C=2
Let,total work =1
work is done by A, \(\frac{1}{A}\)=\(\frac{W(A)}{6}\)= W(A)=\(\frac{6}{A}\)
work is done by B, \(\frac{1}{2A}\)=\(\frac{W(B)}{3}\)= W(B)=\(\frac{3}{2A}\)
work is done by C, \(\frac{1}{3A}\)=\(\frac{W(C)}{2}\)= W(C)=\(\frac{2}{3A}\)
now the proportion of the total work was completed by B
\(\frac{(3|2A)}{(6/A)+(3/2A)+(2/3A)}\)
=\(\frac{9A}{49A}\)
=9/49
IMO C