A and B together can do a piece of work in 30 days, B and C together can do it in 20 days, A starts the work and works on it for 5 days, B takes up and work for 15 days. Finally C finishes the work in 18 days. The number of days in which C alone can do the work where doing it separately is = ?
A. 120 days
B. 40 days
C. 60 days
D. 24 days
Answer: Option D
Solution(By Examveda Team)
L.C.M. of Total Work =60One day work of A + B = $$\frac{{60}}{{30}}$$ = 2 unit/day
One day work of B + C = $$\frac{{60}}{{20}}$$ = 3 unit/day
$$\eqalign{ & {\text{According to the question,}} \cr & \Rightarrow \left( {{\text{A}} + {\text{B}}} \right).....{\text{30 days}} \cr & \Rightarrow \left( {{\text{B}} + {\text{C}}{\text{.}}} \right).....{\text{20 days}} \cr & \Rightarrow {\text{A}}.....{\text{5}} \cr & \Rightarrow {\text{B}}.....{\text{5}} + {\text{10}} \cr & \Rightarrow {\text{C}}.....{\text{10}} + {\text{8 days}} \cr} $$
Work done by (A +B) in 5 days
= 2 × 5 = 10 units
⇒ Work done by (B + C) in 10 days
= 10 × 3 = 30 units
⇒ Total work (finished till now).....40 units
⇒ Remaining work
= 60 - 40
= 20 units
⇒ Here we find that C does remaining 20 units in 8 days
⇒ C's efficiency = $$\frac{{{\text{Work}}}}{{{\text{Day}}}}$$
$$ = \frac{{{\text{20 Work}}}}{{{\text{8 Days}}}} = \frac{5}{2}$$
⇒ Therefore, time taken by C alone to complete the work
$$ = \frac{{60}}{5} \times 2 = 24{\text{ days}}$$
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Comments ( 1 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
More précised solution :
Suppose Total Work is L.C.M of 20 and 30 = 60 unit
Efficiency of A+ B = (60/30) = 2 unit ------Eq-1
Efficiency of (B+C ) =(60/30 ) = 3 unit -------Eq-2
Here , From equation 1 A's efficiency =( 2-B )
From Equation 2 C's efficiency = ( 3-B)
B's efficiency = B
Now ;
5(2-B ) + 15B + 18(3-B) = 60 Unit
solving it B's efficiency =(1/2) unit
So time required by B to complete 60 unit of work = (60/(1/2))= 120 days
In question B+C compete the work together in 20 days thus using formula C's work ={ (B+C)*B}/{B-(B+C)}= (120*20)/(120-20)= 24 days
Answer: C can complete the work in 24 days