Q.1 It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work?
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)
The total no. of days required to complete the work = 1/ 30 or 30 days
Q.2 A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for how many days ?
A) 5 days
B) 6 days
C) 7 days
D) 8 days
The equation portraying the given problem is:
10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was (30-23) i.e.7 days.
Q.3 A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. How many men should be increased, each working now for 10 hours daily, so that the work can be completed in time.
One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)
The remaining work (5/7) has to be completed within 60 days, because the total
number of days allotted for the project is 150 days.
So we get the equation
(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men working
after the 90th day.
We get x = 225
Since we have 75 men already as given in the question,
Then, 225-75= 150
Q.4 It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete?
A) (y – 2) / y
B) 1-y/2 * y
D) None of the above
To type a manuscript karthik took y hours.
Therefore his speed in typing = 1/y.
He was called away after 2 hours of typing.
Therefore the work completed = 1/y * 2.
Therefore the remaining work to be completed = 1 – 2/y.
(i.e.) work to be completed = (y-2)/y
Q.5 If 3 houses are to be painted, Mr. A can paint a house in 6 days (nos are not same) Mr. B can do the same in 8 days & Mr. C in 12 days. If Mr. A does the work for 8 days & leaves for vacation, & Mr. B continues the work for the next 6 days, for how many days should Mr. C work?
1/6 * 8 + 1/8*6 + 1/12 * x =3
Multiply by common denominator of 24
32+18+2x = 72