A is 60% more efficient than B. In how many days will A and B working together complete a piece of work which A alone takes 15 days to finish?
A. $$\frac{{124}}{{13}}$$ days
B. $$\frac{{113}}{{13}}$$ days
C. $$\frac{{108}}{{13}}$$ days
D. $$\frac{{131}}{{13}}$$ days
E. $$\frac{{120}}{{13}}$$ days
Answer: Option E
Solution(By Examveda Team)
Given, A is 60% more efficient of B Means, $$\eqalign{ & {\text{A}} = {\text{B}} + 60\% \,{\text{of B}} \cr & {\text{A}} = {\text{B}} + \frac{{60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{100{\text{B}} + 60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{160{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{8{\text{B}}}}{5} \cr} $$ A can complete whole work in 15 days. So, One day work of A = $$\frac{1}{{15}}$$ One day work of A = $$\frac{{8{\text{B}}}}{5}$$ = $$\frac{1}{{15}}$$ One day work of B = $$\frac{5}{{120}}$$ = $$\frac{1}{{24}}$$ One day work, (A + B) = $$ \frac{1}{{15}} + \frac{1}{{24}}$$ One day work, (A + B) = $$\frac{{24 + 15}}{{360}}$$ = $$\frac{{39}}{{360}}$$So, Time taken to finish the work by A and B together = $$\frac{{360}}{{39}}$$ = $$\frac{{120}}{{13}}$$ days Alternatively We can solve it through percentage method Given, A = $$\frac{{8{\text{B}}}}{5}$$ A can complete whole work in 15 days Work rate of A = $$\frac{{100}}{{15}}$$ = 6.66% per day Work rate of $$\frac{{8{\text{B}}}}{5}$$ = 6.66% Work rate of B = 4.16% per day Work rate of (A + B) = 6.66 + 4.16 = 10.82% per day So, A and B can complete 100% work in $$\frac{{120}}{{13}}$$ days
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Comments ( 7 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
360 ??
#AHAMED SOORAJ as A is 60% more than B,so if B is 100% than A is 160% of B i.e.
A=B×160/100
A=8B/5
A=8/5B . How?????
a is 200% more efficient than b while a takes 60 days less than b to finished a work then in how many days they can finished that work together ?
Any method???
how did 8B come??
Tq so much sir.