A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A. 23 days
B. 37 days
C. $$37\frac{1}{2}$$ days
D. 40 days
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Whole}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & = {20 \times \frac{5}{4}} = 25\,{\text{days}} \cr & {\text{Now}},\,\left( {1 - \frac{4}{5}} \right)\,\,i.e., \cr & \frac{1}{5}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{3}}\,{\text{days}} \cr & {\text{Whole}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}} \cr & = \left( {3 \times 5} \right) = 15\,{\text{days}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{25}}, \cr & \left( {{\text{A + B}}} \right)\,{\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{15}} \cr & \therefore {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} - \frac{1}{{25}}} = \frac{4}{{150}} = \frac{2}{{75}} \cr & {\text{So,}}\,{\text{B}}\,\,{\text{alone}}\,{\text{would}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{75}}{2} = 37\frac{1}{2}\,{\text{days}} \cr} $$Join The Discussion
Comments ( 2 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
For 20% work,
A and A+B take 5 days and 3 days resp.
Then, B takes (5×3)/(5-3)days i.e. 7.5 days
So, for 100% work takes ( 7.5×5) days
Final Answer: 37.5 days.
Thanks !!
80% work done by A= 20 days
100% work will be done 20/80X100=25days
Remaining work 20% do A and B In 3days
100% work work will be completed A&B in 3/20X100=15days
LCM method
A------>25
A&B------->15
LCM 75 so A's efficiency 3 and A&B is 5
B's efficiency 5-3=2
B can do whole work is 75/2=37.5