Ganga and Saraswati, working separately can mow field in 8 and 12 hours respectively. If they work in stretches of one hour alternately. Ganga is beginning at 9 a.m., when will the moving be completed?
A. 6:20 PM
B. 6:30 PM
C. 6:36 PM
D. 6:42 PM
Answer: Option B
Solution(By Examveda Team)
According to question,
Ganga begins at 9 am and she does 3 units/hours
Saraswati begins at 10 am and she does 2 units/hours
So by 11 am they complete 5 units
Time $$ = \frac{{{\text{T}}{\text{.W}}.}}{{3 + 2}} = \frac{{24}}{5}$$
(4 cycle of 2 hrs each + 4 units left)
And now ganga will complete 3 unit out of 4 units in 1 hr
Now, rest 1 unit work done by = $$\frac{1}{2}$$ hr
Total time = 8 + 1 + $$\frac{1}{2}$$ = 9$$\frac{1}{2}$$ hr
Hence, Work finished at
= 9 am + 9$$\frac{1}{2}$$ hr
= 6:30 PM
Alternate Solution:
Work done by Ganga in 1 hour = $$\frac{1}{8}$$
Work done by Saraswati in 1 hour = $$\frac{1}{12}$$
They are working alternatively with Ganga beginning the job.
Work done in every two hours = $$\frac{1}{8}$$ + $$\frac{1}{12}$$ = $$\frac{5}{24}$$
Work done in 4 × 2 = 8 hours = $$\frac{5\times4}{24}$$ = $$\frac{5}{6}$$
Remaining work = 1 - $$\frac{5}{6}$$ = $$\frac{1}{6}$$
In 9th hour, Ganga starts the work and does $$\frac{1}{8}$$ of the work
Work remaining = $$\frac{1}{6}$$ - $$\frac{1}{8}$$ = $$\frac{1}{24}$$
In 10th hour, Saraswati starts the work
Time needed to finish the remaining work
$$\eqalign{ & = \frac{{\frac{1}{{24}}}}{{\frac{1}{{12}}}} \cr & = \frac{1}{{24}} \times 12 \cr} $$
$$=$$ 0.5 hours
$$=$$ 30 minutes
i.e., work will be completed in 9 hour 30 minutes, after 9 AM
i.e., at 6:30 PM
This Question Belongs to Arithmetic Ability >> Time And Work
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Comments ( 14 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
Ganga and Saraswati work completed in 2 hrs=1/8+1/12=5/24 part
2*4=8 hrs=20/24=5/6 part
Remaining=1-5/6=1/6 part which completed by Ganga
Ganga 1/8 part completed in 1 hrs
1/6 '' '' '' 4/3 ''=80 minute=1 hr 20 min
Total time taken=9 hrs 20 min
Moving completed=9 am+ 9 hrs 20 min=6:20 pm
Ans: 6:30 pm
Solution 1
Work done by Ganga in 1 hour = 18
Work done by Saraswati in 1 hour = 112
They are working alternatively with Ganga beginning the job.
Work done in every two hours = 18+112=524
Work done in 4×2=8 hours = 5×424=56
Remaining work =1−56=16
In 9th hour, Ganga starts the work and does 18 of the work
Work remaining = 16−18=124
In 10th hour, Saraswati starts the work
Time needed to finish the remaining work
=(124)(112)=124×12
= 0.5 hour= 30 minutes
i.e., work will be completed in 9 hour 30 minutes, after 9 am
i.e., at 6:30 pm
Answer will be 6:30pm
which is the correct answer?
The correct answer will be 6:20PM
6.20 pm
Please correct your answer it makes a lots of confusion
yes ans will be option bthat is 6:30.
logically these are wrong method to solve that answer,because in both case we assumed that they work together and time will be doubled but the last remaining work of savitri's turn would complete in half an hour only,i.e. (1=1/2) is differ from {(1=1)/2}
answer will be 6:30pm
method:
ganga =8 days
savitri = 12 days
LCM of 8 and 12= 24unit
efficiency of ganga and savitri are 3 and 2 respectively.
with 5(3+2) unit of efficiency 20 unit of work can completed in 4*2=8days
then the next turn for ganga finish next 3 unit of work in next one hour, agin the remaining 1unit of work finished by savitri in 1/2 hour, because savitri's efficiency is 2 unit in an hour
The answer will be 9:30.
Because after 9 hrs work will be 4(1/8+1/12) +1/8 as Ganga started first.
Work left would be 1/24 for saraswati and she will do it in 12/24 i.e. 30 mins.
So total time will be 9:30 and time would be 6:30.
How will come 24*2/5???
How come 24*2/5 is 9.5???? its 9.60. please don't do wrong calculations
24/5 would be 4 4/3. Now the 4 hours would become 8 (as per alternative hour principle) and the remaining 4/3 can be written as 1 1/3. So 8 + 1 would become 9 hours now only 1/3 left which will become 20 mins.
I think the answer would be 9hrs and 20 mins but it's not there in the option