Miscellaneous Test: Time & Work- 3

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24 men working 8 h a day can finish a work in 10 days. Working at a rate of 10 h a day, the number of men required to finish the work in 6 days is


24 × 8 × 10 = N × 10 × 6 Æ N = 32


12 men complete a work in 18 days. 6 days after they had started working, 4 men join them. How many more days will all of them take to complete the remaining work?


12 × 18 = 12 × 6 + 16 × t Æ t = 9


A cistern is normally filled in 6 h but takes 4 h longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in how much time?


The cistern fills in 6 hours normally, means that the rate of filling is 16.66% per hour. With the
leak in the bottom, the rate of filling becomes 10% per hour (as it takes 10 hours to fill with the
This means that the leak drains out water at the rate of 6.66% per hour. This in turn means that the
leak would take 100/6.66 = 15 hours to drain out the entire cistern.


There are two pipes in a tank. Pipe A is for filling the tank and Pipe B is for emptying the tank. If A can fill the tank in 10 hours and B can empty the tank in 15 hours then find how many hours will it take to completely fill a half empty tank?


A’s work = 10%
B’s negative work = 6.66%
(A + B)’s work = 3.33%
To fill a half empty tank, they would take 50/3.33 = 15 hours.


A, B and C can do some work in 36 days. A and B together do twice as much work as C alone and A and C together can do thrice as much work as B alone. Find the time taken by C to do the whole work.


(A + B) = 2C.
Also,(A + C) = 3B
36(A + B + C) = 1
Solving for C, we get:
36 (2C + C) = 1 Æ 108C = 1
C = 1/108
Hence, C takes 108 days.


Two taps are running continuously to fill a tank. The 1st tap could have filled it in 5 hours by itself and the second one by itself could have filled it in 20 hours. But the operator failed to realise that there was a leak in the tank from the beginning which caused a delay of one hour in the filling of the tank. Find the time in which the leak would empty a filled tank.


Without the leak:
Rate of work = 20% + 5% = 25%. Thus, it would have taken 4 hours to complete the work.
Due to the leak the filling gets delayed by 1 hour. Thus, the tank gets filled in 5 hours. This means
that the effective rate of filling would be 20% per hour. This means that the rate at which the leak
empties the tank is 5% per hour and hence it would have taken 20 hours to empty a filled tank.


Two forest officials in their respective divisions were involved in the harvesting of tendu leaves.One division had an average output of 21 tons from a hectare and the other division, which had 12 hectares of land less, dedicated to tendu leaves, got 25 tons of tendu from a hectare. As a result,the second division harvested 300 tons of tendu leaves more than the first. How many tons of tendu leaves did the first division harvest?


25 (n – 12) = 21 n + 300. Solving this equation, n = 150. Hence, the first division harvest 3150


Dev and Tukku can do a piece of work in 45 and 40 days respectively. They began the work together, but Dev leaves after some days and Tukku finished the remaining work in 23 days. After how many days did Dev leave


n(1/45 + 1/40) + 23/40 = 1 Æ n = 9.


Ajit can do as much work in 2 days as Baljit can do in 3 days and Baljit can do as much in 4 days as Diljit in 5 days. A piece of work takes 20 days if all work together. How long would Baljittake to do all the work by himself?


Let Ajit’s rate of work be 100/2 = 50 work units per day. Baljit would do 100/3 = 33.33 work
units per day and Diljit does 133.33/5 = 26.66 units of work per day. Their 1 days work = 50 +
33.33 + 26.66 = 110 units of work per day. In 20 days, the total work done would be 2200 units of
work and hence for Baljit to do it alone it would take: 2200/33.33 = 66 days to complete the same


A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5gallons/min. The outlet of the tank is twice the diameter of the inlet. How many minutes will it take to empty the tank if the inlet is shut off when the tank is full and the outlet is opened? (Hint: Rate of filling or emptying is directly proportional to the diameter)


The outlet pipe will empty the tank at a rate which is double the rate of filling (Hence, 10 gallons
per minute). If the inlet is shut off, the tank will get emptied of 100 gallons of water in ten minutes.


X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.


XÆ12 days Æ 8.33% of the work per day.
Y Æ 18 days Æ 5.55% of the work per day
Z Æ 10 days Æ 10% of the work per day.
In three days, the work done will be 25 + 16.66 + 30 = 71.66%. The remaining work will get
done by Y in 28.33/5.55 = 5.1 days.
[Note: You need to be fluent with your fraction to percentage conversions in order to do well at
these kinds of calculations.]


Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger’s work in 10 days is equal to the first digger’s work in 14 days. How many metres does the first digger dig per shift?


The per day digging of all three combined is 54 meters. Hence, their average should be 18. This
means that the first should be 18 – x, the second, 18 & the third 18 + x.
The required conditions are met if we take the values as 15,18,21 meters for the first, second and
third diggers respectively. Hence, (a) is the correct answer.


Two typists of varying skills can do a job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 minutes, they would be left with 1/5 of the whole work. How many minutes would it take the slower typist to complete the typing job working alone?


Since the first typist types for 4 minutes and the second typist types for exactly 6 minutes, the work
left (which is given as 1/5 of the total work) would be the work the first typist can do in 2 minutes.
Thus, the time taken by the first typist to do the work would be 10 minutes and his rate of work
would be 10% per minute. Also, since both the typists can do the work together in 6 minutes, their
combined rate of work would be 100/6 = 16.66% per minute.
Thus, the second typist’s rate of work would be 16.66 – 10 = 6.66% per minute.
He would take 100/6.66 = 15 minutes to complete the task alone.


It takes six days for three women and two men working together to complete a work. Three men would do the same work five days sooner than nine women. How many times does the output of a man exceed that of a woman?


Solve this using options. If we check for option (c) i.e. the work of a man exceeds the work of a
woman by 5 times, we would get the following thought process:
Total work = 6 days × (3 women + 2 men) = 18 woman days + 12 man days = 18 woman days +
60 woman days = 78 woman days.
Thus, 9 women would take 78/9 days = 8.66 days and hence 3 men should do the same work in
3.66 days. This translates to 3 × 3.66 = 10 man days or 50 woman days which is incorrect as the
number of woman days should have been 78.
Thus, we can reject this option.
If we check for option (d) i.e. the work of a man exceeds the work of a woman by 6 times, we
would get the following thought process:
Total work = 6 days × (3 women + 2 men) = 18 woman days + 12 man days = 18 woman days +
72 woman days = 90 woman days.
Thus, 9 women would take 90/9 days = 10 days and hence 3 men should do the same work in 5
days. This translates to 3 × 5 = 15 man days or 90 woman days which is correct as the number of
woman days should be 90.
Thus, we select this option.


Two pipes A and B can fill up a half-full tank in 1.2 hours. The tank was initially empty. Pipe B was kept open for half the time required by pipe A to fill the tank by itself. Then, pipe A was kept open for as much time as was required by pipe B to fill up 1/3 of the tank by itself. It was then found that the tank was 5/6 full. The least time in which any of the pipes can fill the tank fully is


The interpretation of the first statement is that (a) & (b) do 41.66 percent of the work per hour.
From this point if we go through the options, option (b) fits the situation as 4 hours per one person means 25 percent work per hour per person. Consequently this means 16.66 percent per work per hour per other person.

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