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X Can finish a piece of work in 12 days while Y can do it in 15 days. If both work at it together. How much time will they take to do the work?
Efficiency of A = 100 / 12 = 8.33%
Efficiency of B = 100 / 15 = 6.66%
Combined efficiency of A and B = 8.33 + 6.66 = 15%
Number of days taken by A and B, when working together = 100 / 15 =
Note : Efficiency x Time period = Fixed amount of work
Also, in terms of percentage total work to be done is considered as 100% (in fraction it is 1), unless otherwise stated.
Alternatively : It can be done through unitary method, also.
X can do piece of work in 5 days. Y can do it in 10 days. With the help of Z, they finish the work in 2 days. In how many days Z alone can do the whole work?
►Efficiency of A = 20% = 100 / 5
►Efficiency of B = 10% = 100 / 10
►Efficiency of A,B and C = 50%
►∴ Efficiency of C = (Efficiency of A,B and C) – (Efficiency of A and B) = (50)  (20 + 10) = 20%
►∴ Number of days required by C to work alone = 100 / 20 = 5 days
►Alternatively: Go through options and satisfy the values.
A is thrice as good a work man as B and takes 10 days less to do a piece of work than B takes. The number of days taken by B to finish the work is:
(Since number of days are inversely proportional to the efficiency)
Now if A requires x days, so B requires 3x days.
∴ Difference of required days = (3x  x) = 2x = 10
► ⇒ x = 5
Hence the number of days required by
► B = 3x = 3 x 5 = 15 days
Ajit is 3 times as efficient as Bablu, then the ratio of number of days required by each to work alone, completely?
A is thrice as efficient as B. Working together they complete the work in 3 days. If B takes 8 days more than A, what is the number of days taken by A to finish the whole work, alone?
Efficiency of A + B = 33.33% = (100 / 3)
Ratio of efficiency of A and B = 3 : 1
∴ Efficiency of A =
∴ Number of days taken by A = 4 = 100 /25
Alternatively :
∴ Difference in days = 2x = 8
► ⇒ x = 4 and 3x = 12
Therefore number of days taken by A, working alone = 4 days
Alternatively :
Now, you can use the options, or solve the equations to get the value of x which is equal to 4.
Ganga, Jamuna and Saraswati can do a piece of work, working together, in 1 day. Ganga is thrice efficient as Jamuna and Jamuna takes the twice the number of days as Saraswati takes to do it alone. What is the difference between the number of days taken by Ganga and Saraswati?
Remember
Now,
Again, efficiency of Ganga, Jamuna and Saraswati
= 100 / 1 = 100%
∴ Efficiency of Ganga =
Efficiency of Saraswati =
Now, number of days taken by Ganga
= 100 / 50 = 2
Number of days taken by Saraswati
= 100 / 33.33 = 3
∴ Difference in number of days taken by Ganga and Saraswati
= 3  2 = 1 day
A and B can complete a task in 30 days when working together. After A and B have been working together for 11 days, B is called away and A, all by himself completes the task in the next 28 days. Had A been working alone from begining, the number of days taken by him to complete the task would have been:
Work done in 11 days = 11 / 30
Rest work = 19 / 30
1 day's work of A =
Total number of days required to complete the whole work alone.
Efficiency of Asha is 25% more than Usha and Usha takes 25 days to complete a piece of work, Asha started a work alone and then Usha joined her 5 days before actual completion of the work. For how many days Asha worked alone?
∴ Number of days required by Asha to finish the work alone = 20
► ∴ (4 x = 4 x 5)
(Alternatively, from percentage change graphic, number of days taken by Asha will be 20% less than Usha, if efficiency of Asha is 25% more than Usha)
Now, since Asha and Usha did work together for last 5 days = 5 x 9 = 45%
(Since efficiency of Asha = 5% and Usha's efficiency = 4%)
It means Asha completed 55% work alone
∴ Number of days taken by Asha to complete 55% work = 55 / 5 = 11
Chandni and Divakar can do a piece of work in 9 days and 12 days respectively. If they work for a day alternatively, Chandni beginning, in how many days, the work will be completed?
Efficiency of Chandni = 11.11%
Efficiency of Divakar = 8.33%
They do 19.44% work in 2 days.
∴ They need 10 days to do 97.22% work,
Now the rest work (2.78) was done by Chandni in 2.78 / 11.11 = 1 / 4 days
Therefore total number of days required =
Alternatively :
Chandni's one day's work = 1 / 9
Divakar's one day's work = 1 / 12
Chandni's and Divakar's (1 + 1) = 2 day's work = 1 / 9 + 1 / 12 = 7 / 36
So, in 10 days they do =
So, the remaining work will be done by Chandni =
Thus total number of required days =
Hint
A group of men decided to do a job in 4 days. 20 men dropped out from the task every day due to which work was completed in 7 days. How many men were there at the beginning?
Let X be the initial number of men then,
According to the question,
4X = X + (X  20) + (X  40) + (X  60) + (X  80) + (X  100) + (X  120)
⇒ 4X = 7X  420
⇒ 3X = 420
⇒ X = 420/3
⇒ X = 140 men
The number of days required by A,B and C to work individually is 6, 12 and 8 respectively. They started a work doing it alternatively. If A has started then followed by B and so on, how many days are needed to complete the whole work?
► 6 / 8 = 3 / 4
In 3 days A,B,C do 3 / 8 work,
In 6 days A,B,C do 3 / 4 work
Rest work = 1 / 4, which is less than 3 / 8, On the 7th day, 1 / 6 more work will be done by A
Now rest work =
Now, this rest work (1 / 12) will be done by B in 1 complete day.
Thus, total number of days = 6 + 1 + 1 = 8 days.
Alternatively : Efficiency of A = 16.66% , Efficiency of B = 8.33% , Efficiency of C = 12.5%
Efficiency of A + B = 25% , Efficiency of A + B + C = 37.5%
In 3 days A,B,C completes 37.5% work, In 6 days A,B,C completes 75% work
Rest work = 25%
This 25% work will be completed by A and B in next 2 days, Thus total 6 + 2 = 8 days are needed.
When A,B and C are deployed for a task, A and B together do 70% of the work and B and C together do 50% of the work. Who is most efficient?
A + B = 70%
B + C = 50%
⇒ B = 20% , A = 50% and C = 30%
Hence, A is most efficient.
Sharma is 20% less efficient than Kelkar. If Kelkar can do a piece of work in 24 days. the number of days required by Sharma to complete the same work alone will be—
► ∴ 0.8k = 24 ⇒ k = 30
Thus Sharma requires 30 days, to complete the work, alone.
If 10 persons can do a job in 20 days, then 20 person with twice the efficiency can do the same job in:
M x D = 10 x 20 = 200
Mandays New Mandays = (20 x 2) x x
► 200 = 20 x 2 x x
► x = 5 days
or M_{1}D_{1} = M_{2}D_{2}
► 10 x 20 = (20 x 2) x x
► ⇒ x = 5
30 workers can finish a work in 20 days. After how many days should 9 workers leave the job so that the work is completed in total 26 days :
Go through options. Consider option (c)
► 30 x 20 = 30 x 6 + 21 x 20
► 600 = 600,
Hence presumed option is correct.
Alternatively :
► 30 x 20 = 30 x x + 21 x (26  x )
► ⇒ x = 6
Mr. Modi can copy 40 pages in 10 minutes, Mr. Xerox and Mr. Modi both working together can copy 250 in 25 minutes. In how many minutes Mr. Xerox can copy 36 pages?
Efficiency (per minute) of Modi = 4 copies/min
Efficiency of Modi and Xerox together = 10 pages/min
∴ Efficiency of Xerox alone = 10  4 = 6 pages/min
∴ Mr. Xerox needs 6 minutes to copy 36 pages.
6 children and 2 men complete a certain piece of work in 6 days. Each child takes twice the time taken by a man to finish the work. In how many days will 5 men finish the same work?
6C + 2 M = 6 days
► ⇒ 36C + 12 M = 1 day
Again 1M = 2C
► ∴ 36 + 12 x 2 = 1 day
60 children can do the work in 1 day Now,
► 5 men = 10 children
∴ 10 children can do the work in 6 days.
Directions for question : A can do a work in 15 days and B can do it in 18 days. with the help of C work is completed in 6 days.
Q. How long will it take for C to finish the work alone?
Efficiency of A = 6.66% , Efficiency of B = 5.55% , Efficiency of A + B + C = 16.66%
∴ Efficiency of C = 4.44%
Now, number of days required by C =
Directions for question : A can do a work in 15 days and B can do it in 18 days. with the help of C work is completed in 6 days.
Q. A,B and C received total ₹ 27,000 for the whole work. What is the share of B, if the money is distributed in the ratio of amount of work done, individually?
Correct Answer : B
Explanation : A = 15 days
B = 18 days
C = 6 days
Taking LCM, we get 180
Efficiency of A = 12
Efficiency of B = 10
Efficiency of A+B+C = 6
A.T.Q
=> (10/30)*27000
= 9000
314 weavers weaves 6594 shawls in 1 / 6 hours. What is the number of shawls weaved per hour by an average weaver?
In 1 hour 314 weavers weave = 6594 x 6
shawls In 1 hour 1 weavers weave = = 126 shawls
If 20 engineers and 20 workers can together construct a 20 km road in 20 days. 40 engineers and 40 workers together will construct 40 km road in how many days?
Equate the mandays
For 20 km road, 20 x 20 = 400 mandays are required
∴ For 40 km road 800 mandays are required So, 800 = 40 * x
► ⇒ x = 20
A man, a woman and a girl worked for a contractor for the same period. A man is twice efficient as a woman and a woman is thrice efficient as a girl. ₹ 10000 were given to all of them. What is the sum of money received by a woman and a girl together?
Efficiency of a man : woman : girl = 6 : 3 : 1
∴ Share of a woman and girl =
=
There was a leakage in the container of the refined oil. If 11 kg oil leaks out per day then it would have lasted for 50 days, if the leakage was 15 kg per day, then it would have lasted for only 45 days. For how many days would the oil have lasted, if there was no leakage and it was completely used for eating purpose?
Let x kg of oil is used for eating purpose, daily, then
► (x + 11) x 50 = + 15 x 45
► x = 25
∴ Total quantity of oil = (25 + 11) x 50 = 1800
∴ Required number of days = 1800 / 25 = 72
Tap A can fill a tank in 20 hours, B in 25 hours but tap C can empty a full tank in 30 hours. Starting with A, followed by B and C each tap opens alternatively for one hour period till the tank gets filled up completely. In how many hours the tank will be filled up completely?
Correct Answer : d
Explanation : LCM(20,25,30)=300
Suppose capacity of the tank is 300 litre.
Quantity filled by tap A in 1 hour
= 300/20
= 15 litre.
Quantity filled by tap B in 1 hour = 300/25
= 12 litre.
Quantity emptied by tap C in 1 hour = 300/30
= 10 litre.
In every three hour, 15 + 12 − 10 = 17 litre is filled.
In 45 hours,
17 × 15 = 255 litre is filled.
Remaining quantity to be filled = 300 − 255 = 45 litre.
In next 3 hour, 17 more litre is filled.
Remaining quantity to be filled = 45 − 17 = 28 litre.
In next 2 hour hour, 15 + 12 = 27 more litre is filled.
Remaining quantity to be filled = 28 − 27 = 1 litre.
But in next 1 hour, 10 litre is emptied.
Remaining quantity to be filled = 1 + 10
= 11 litre.
Pipe A fills this remaining quantity in 11/15hour (i.e, in 44 minutes).
Therefore, the tank is filled in 51 hour 44 minutes
Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hours working separately. Pipe C can empty the whole tank in 4 hours. Ramesh opened the pipe A and B simultaneously to fill the empty tank. He wanted to adjust his alarm so that he could open the pipe C when it was halffilled, but he mistakenly adjusted his alarm at a time when his tank would be 3/4th filled. What is the time difference between both the cases, to fill the tank fully.
In ideal case :
Time taken to fill the half tank by A and B = 50 / 41.66 = 6 / 5 hours
Time taken by A,B and C to fill rest half of the tank = 50 / 16.66 = 3 hours
Total time =
In second case :
Time taken to fill 3 / 4 tank by A and B = 75 / 41.66 = 9 / 5 hours
Time taken by A,B and C to fill rest 1 / 4 tank = 25 / 16.66 = 3 / 2 hours
Total time = 9 / 5 + 3 / 2 = 3 hours 18 minutes
Therefore, difference in time = 54 minutes
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