P and Q together can do a job in 6 days. Q and R can finish the same job in $$\frac{{60}}{7}$$ days. P started the work and worked for 3 days. Q and R continued for 6 days to finish the work. Then the difference of days in which R and P can complete the alone is P can complete the job alone is ?
A. 10 days
B. 8 days
C. 12 days
D. 15 days
Answer: Option A
Solution(By Examveda Team)
L.C.M. of Total Work = 60One day work of P + Q = $$\frac{{60}}{{6}}$$ = 10 unit/day efficiency
One day work of Q + R = $$\frac{{60}}{{\frac{{60}}{7}}}$$ = 7 unit/day efficiency
$$\eqalign{ & \left( {{\text{Q}} + {\text{R}}} \right){\text{ 6 days work}} \cr & = 7 \times 6 \cr & = 42{\text{ units}} \cr} $$
Then in 3 days = total work = 18
$$\eqalign{ & {\text{P completes}} \cr & = 60 - 42 \cr & = 18{\text{ units}} \cr & {\text{P's efficiency}} \cr & = \frac{{18}}{3} \cr & = 6{\text{ units/day}} \cr & {\text{Q's efficiency}} \cr & = 10 - 6 \cr & = 4{\text{ units/day}} \cr & {\text{R's efficiency}} \cr & = 7 - 4 \cr & = 3{\text{ units/day}} \cr & {\text{P completes whole work in}} \cr & = \frac{{60}}{6} \cr & = {\text{10 days}} \cr & {\text{R completes whole work in}} \cr & = \frac{{60}}{3} \cr & = {\text{20 days}} \cr & {\text{Difference is}} \cr & = \left( {20 - 10} \right) \cr & = 10{\text{ days }} \cr} $$
Join The Discussion
Comments ( 1 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
Let,P takes =X days
Q takes =Y days
R takes=Z days
P Can do in 1 Day=1/X part
Q can do in 1 Day=1/Y part
R Can do in 1 day=1/Z part
1st condition,
1/X+1/Y=1/6 ------(1)
2nd Condition,
1/Y+1/Z=7/60 ------(2)
3rd Condition,
3*(1/X)+ (1/Y+1/Z)*6=1
3/X+(7/60)*6=1 [(1/Y+1/Z)=7/60]
X=10
So P takes 10 days to complete task alone.
Ans.10 Days(A)