If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in:
A. 18 days
B. 24 days
C. 30 days
D. 40 days
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}} \cr & \left( {A + B} \right) = \frac{1}{{18}}\,.......(1) \cr & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}} \cr & \left( {A + C} \right) = \frac{1}{{12}}\,.......\left( 2 \right) \cr & {\text{One}}\,{\text{day's}}\,{\text{work}}\,{\text{of}} \cr & \left( {B + C} \right) = \frac{1}{9}\,.......\left( 3 \right) \cr & {\text{Adding}}\,\left( {\text{1}} \right){\text{,}}\,\left( {\text{2}} \right)\,{\text{and}}\,\left( {\text{3}} \right) \cr & 2 \times \left( {A + B + C} \right) = { {\frac{1}{{18}}} + {\frac{1}{{12}}} + {\frac{1}{9}} } \cr & 2(A + B + C) = \frac{1}{4} \cr & {\text{One day's work of}} \cr & {A + B + C} = \frac{1}{8} \cr & B = {\frac{1}{8}} - \left( {A + C} \right) \cr & B = {\frac{1}{8}} - {\frac{1}{{12}}} \cr & {\text{One day's work of}} \cr & B = \frac{{ {3 - 2} }}{{24}} = \frac{1}{{24}} \cr & B\,{\text{need}}\,24\,{\text{days}} \cr} $$This Question Belongs to Arithmetic Ability >> Time And Work
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Comments ( 11 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
A+B----18 days
A+c------12days
B+C------9days
B-----?
LCM of 18,12,9=36
A+B-----36/18=2units
A+C-----36/12=3units
B+C------36/9=4units
______________________
2(A+B+C)=9
A+B+C=9/2
A+B+C=4.5
A+4=4.5
A=4-4.5= 0.5
2+C=4.5
C=4.5-2=2.5
B+3=4.5
B=4.5-3=1.5
B alone 36/1.5=24 days
A+B=15
B=20
Total work =60days
A+B=4 unit
B=3unit,
A alone =?
A alone=(A+B)-B
=4-3
=1 unit/day
A total time =total work /total efficiency
=60/1
=60 days (ans)
4th step, why take a 2 which is put at multiplication
My dear genius can explain me 1/18+1/12+1/9=1/4 how?
A+B=18 days =1/18
A+C=12 days=1/12
B+C=9 days =1/9
LCM of 18,12and 9 is 36
18×2=36
12×3=36
9×4=36
To get the answer we need to Multiple 2×3×4=24 (which can be written 1/24)
Points to remember
1.Time and work is always opposite to each other
2. If numerator is greater then 1 we need to change it to get the Answer Example if Answer was 2/24 we would have changed 24/2 to get the Answer =12
4th step why take a 2
Take LCM of 18,12,9 that is 36
So if total work is 36
A+B do 36/18= 2work per day
A+C do 3
B+C do 4
Adding both sides we get
2(A+B+C)= 9
A+B+C= 9/2
B+3= 9/2 (as A+C=3)
Or B= 3/2
So B do 3/2 works per day
So B will do total work that is 36, in 36÷3/2= 24 days
Bigboy
2(a+b+c) is come because we add three equation
(A+b)+(A+c)+(B+c)=2a+2b+2c=2(a+b+c)
Same as right side
1/18+1/12+1/9=9/36
So right side=left side
2(a+b+c)=1/4
a+b+c=1/8
Excuse me guys how it comes A+B+C = 1/8
whats that mean 2*(a+b+c)... please help
Please explain in shortcut
Please explain another shortcut method