A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?
A. 24 days
B. 25 days
C. 27 days
D. 30 days
Answer: Option A
Solution(By Examveda Team)
Let the work be completed in x days. C work for x days then A works for (x - 8) days and B works for (x - 12) days. According to the question,$$\eqalign{ & {\frac{{ {x - 8} }}{{36}} + \frac{{ {x - 12} }}{{54}} + \frac{x}{{72}}} = 1 \cr & {\frac{{ {6x - 48 + 4x - 48 + 3x} }}{{216}}} = 1 \cr & 13x - 96 = 216 \cr & 13x = 216 + 96 = 312 \cr & x = \frac{{312}}{{13}} \cr & x = 24\,{\text{days}} \cr} $$
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Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
36,54,72. 36/6=6
54/9=6
72/12=6
6+6+6=18
72*6=432/18=24
Ans:-24 days
Please find 3 methods to do this Q :
Method 1:
R S T
Time 36 54 72
LCM = total work = 216 units
Eff 6 : 4 : 3
Let work completes in x days, R left 8 days before so he worked for (x-8) days , S left 12 days before so he worked for (x-12) days & T did not leave in between so he worked for all x days.
So ATQ, R*(x-8) +S*(x-12) + T*x = 216
6*(x-8) +4*(x-12) + 3*x = 216
6x - 48+4x-48+3x = 216
13x - 96 = 216
13x = 216+96 = 312
x = 24
Hence T worked for 24 days.
Method 2:
R S T
Time 36 54 72
LCM = total work = 216 units
Eff 6 : 4 : 3
Work-done in last 12 days = T*12+R*(12-8) =3*12 + 6*4 = 36+24 = 60 units
Hence remaining work is done by all initially in = (216 - 60)/(6+4+3) = 156/13= 12 days
So total days = 12 + 12 = 24 days
Hence T worked for 24 days.
Method 3:
R S T
Time 36 54 72
Let work completes in x days, R left 8 days before so he worked for (x-8) days , S left 12 days before so he worked for (x-12) days & T did not leave in between so he worked for all x days.
Hence , 1/36 * (x-8) + 1/54 * (x-12) + 1/72 * (x) = 1
(x-8)/36 + (x-12)/54 + x/72 = 1
{6(x-8) + 4(x-12) + 3x}/216 = 1
6x - 48 + 4x - 48 + 3x = 216
13x - 96 = 216
13x = 216 + 96 = 312x = 24
Hence T worked for 24 days.
Siddu hugar we assume a complete of work os equal to 1
In above equation why the RHS is equal to one.
A can complete a job in 36 days.B is twice as efficient as A. A started the work and was joined by B after a few days. If the whole work was completed in 15 days, after how many days from the time A started working did B join with A sir pls tell me how to solve the
A can do the work in 36 days, B is 20% more efficient than A.If A started then work , worked for 8 days and left, then B can complete the work in how many days