Miscellaneous Test: Time & Work- 3 - Mechanical Engineering MCQ

24 × 8 × 10 = N × 10 × 6 Æ N = 32

12 × 18 = 12 × 6 + 16 × t Æ t = 9

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
leak).
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.

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) = 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.

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.

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

n(1/45 + 1/40) + 23/40 = 1 Æ n = 9.

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
work.

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.

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.]

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.

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.

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.

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.