1. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?
(a) A and B
(b) A and C
(c) B and C
(d) A and D
(e) C and D
Sol. Work done in one day by A, B and C are 1/4,1/8,1/16 and 1/32 respectively.
Using answer choices, we note that the pair of B and C does 3/16 of work in one day; the pair of A and D does 1/4+1/32=9/32 of work in one day
Hence, A and D take 32/9 days
B and C take 16/3=32/6 days
Hence, the first pair must comprise of A and D.
2. R finishes a work in 7 days. P finishes the same job in 8 days and Q in 6 days. They take turns to finish the work. R worked on the first day, P on the second day and Q on the third and then again R and so on. Who was working on the last day when work got finished?
(a) R
(b) P
(c) Q
(d) P and Q
(e) Cannot be determined
Sol. Three day’s work = 1/7+1/8+1/6=73/168
Six day’s work = 73/84
Seventh day work = 1/7, done by R
Since 73/84+1/7=85/84 > 1, therefore, R was working on the last day.
3. Construction of a road was entrusted to a civil engineer. He has to finish the work in 124 days for which he employed 120 workers. Two-third of the work was completed in 64 days. How many workers can be reduced now without affecting the completion of the work on time?
(a) 56
(b) 64
(c) 80
(d) 24
(e) None of these
Sol. 2/3rd of the work was completed in 64 days by 120 workers.
1/3rd of the work was completed in 32 days by 120 workers.
Also 1/3rd of the work is to be completed in 60 days by (120 – x) workers, where x is the number of men reduced in order to finish the work on schedule.
So, (120 – x) × 60 = 120 ⇒ x = 56.
4. Two workers earned Rs. 225 first worked for 10 days and the second for 9 days. How much did each of them get daily if the first worker got Rs. 15 more for working 5 days than the second worker got for working 3 days?
(a) Rs. 11.70; Rs. 12.00
(b) Rs. 10.80; Rs. 13.00
(c) Rs. 11.25; Rs. 12.50
(d) Rs. 12.60; Rs. 11.00
(e) None of these
Sol. Let A got Rs. x per day and B got Rs. y per day. So, 10x + 9y = 225 and 5x = 3y + 15 ⇒ x = 10.80, y = 13.
5. Two pipes A and B can fill a tank in 20 and 30 h respectively. Both the pipes are opened to fill the tank but when the tank is 1/3 full, a leak develops in the tank. Due to this leakage one-third of the water supplied by pipes A and B goes waste. What is the total time to fill the tank if the leak if not closed ?
(a) 12 h
(b) 16 h
(c) 18 h
(d) 20 h
(e) None of these
Sol. Let us assume total work = 180 (we are not assuming it to be LCM of 20 and 30 = 60 because in that case 1/3rd of A + B will be fractional)
Time taken to fill 1/3rd of the tank = 180/ (9 + 6) = 4 h
Due to leakage, net inflow = 2/3 (9 + 6) = 10 units
Time taken to fill remaining 120 units = 12 h
So total time taken = 12 + 4 = 16 h
6. P, Q and R can do a piece of work in 16, 24 and 30 days respectively. They started the work simultaneously but P stops the work after 4 days and Q called off the work 2 days before the completion. In what time the work is finished ?
a) 100/9 days
b) 100/11 days
c) 100/7 days
d) 100/13 days
e) None of these
Sol. 4/16 + (T -2)/24 + T/30 = 1 where T is the time taken to complete the job.
T = 100/9 days.
7. If P can do 1/3 of the work in 5 days and Q can do 1/4 of the work in 6 days, then how much money will Q get if they were paid a total of 390 rupee?
a) 120
b) 150
c) 170
d) 190
e) None of these
b) 150
c) 170
d) 190
e) None of these
Sol. P can alone complete the whole work in 15 days and Q can complete the same work alone in 24 days. So ratio of work done by them 1/15: 1/24 i.e. 8: 5
Q get = (5/13)*390 = 150.
Q get = (5/13)*390 = 150.
8. A does half as much work as B in one third of the time taken by B. If together they take 20 days to finish the work then what will be the share of A if 1000 rupees is given for the whole work?
a) 400
b) 500
c) 600
d) 700
e) None of these
b) 500
c) 600
d) 700
e) None of these
3/2x + 1/x = 1/20
X = 50. So A will complete the work in 100/3 days and B will complete the work in 50 days.
Ratio of work done by A and B – 3/100: 1/50 = 3:2
So A share = 3/5*1000 = 600.
9. A does half as much work as B does in one sixth of the time. If together they take 20 days to complete the work, then what is the time taken by A to complete the work independently.
a) 80/3 days
b) 100/3 days
c) 60/3 days
d) 140/3 days
e) None of these
b) 100/3 days
c) 60/3 days
d) 140/3 days
e) None of these
Sol. Let B complete the work in X days so in one day work done by B is 1/x
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days.
as A do half work in one-sixth of the time so A will complete work in 2*x/6 = x/3 days
One day work of A and B i.e. 3/x + 1/x = 1/20. So we get x = 80
So time taken by A alone = 80/3 days.
10. A and B can do a piece of work in 20 and 25 days respectively. They began to work together but A leaves after some days and B completed the remaining work in 12 days. Number of days after which A left the job-
a) 5.7/9 days
b) 6.7/9 days
c) 7.7/9 days
d) 11.7/9 days
e) None of these
b) 6.7/9 days
c) 7.7/9 days
d) 11.7/9 days
e) None of these
Sol. (1/20 + 1/25)*T + 12/25 = 1
We will get T = 52/9 i.e. 5.7/9 days.
We will get T = 52/9 i.e. 5.7/9 days.
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