To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
A. 30 days
B. 35 days
C. 40 days
D. 45 days
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{We have}} \cr & {\text{B}} = \frac{3}{2} \times {\text{A}} \cr & \to {\text{A}} = \frac{2}{3} \times {\text{B}} \cr & {\text{One day's work,}} \cr & \Rightarrow {\text{A}} + {\text{B}} = \frac{1}{{18}} \cr & \Rightarrow \frac{2}{3} \times {\text{B}} + {\text{B}} = \frac{1}{{18}} \cr & \Rightarrow \frac{5}{3} \times {\text{B}} = \frac{1}{{18}} \cr & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}}\,{\text{B}} \cr & = \frac{3}{{90}} \cr} $$B alone can complete the work in
$$\eqalign{ & = \frac{{90}}{3} \cr & = 30\,{\text{days}} \cr} $$
This Question Belongs to Arithmetic Ability >> Time And Work
Join The Discussion
Comments ( 15 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
A=150 ,B=100
LCM=300, then efficiency of A & B is 2,3
total efficiency =5
B alone can complete the work in =18*5/3
=30 day
Let B takes x days to complete the work
Then A will take 50% more i.e 150℅ of x days i.e 3/2x days.
So the one day work of A and B together will be
1/x +1/(3/2x) = 1/18
1/x + 2/3x = 1/18
5/3x = 1/18
x = 30
I.e B takes 30 days to complete the work.
Time taken by A and B = 3:2
Efficiency = 2:3
Efficiency ×day = Total work
Total work =18×5 =90 (2+3=5)
Complite by B = 90÷3= 30 day
Thank you
Thank u Mesba Milon for good clarification.
Time taken by B= x days
So, time taken by A=3x/2 days
ATQ, 2/3x+1/x=1/18
or, 5/3x=1/18
or, x=30
B alone can complete the work in 30 days.
Capacity Ratio will be a:b=2:3
(a+b) 1 day work=1/18
Than b 1 day work portion =3/5*1/18=1/30
B can do --- 1/30 portion in 1 day
Than -------whole or 1 portion in 30 days.(ans)
Can we get answer by using this method
Effi.of b × Time b = Effi of a+b × Time a+b
Let A=x,B=x/2 ,I got B=27,whats wrong with this please explain any one knows.
Thanks
How u get B=3/2*A plz tell
Let us assume B is 100%of x then A takes 150%of x. so time in ratio of A:B is 100%ofx: 150%ofx= 3x:2x.... if they together works then one days work is 1/3x+1/2x= 1/18 by solving we get x=15 therefore b takes 2x= 2*15= 30 days whereas A takes 45 days......
Where are you getting problem? @Pratibha? I mean, where is the exact point?
explain in deatail
THANKS