Exercise : 1


1. 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 34 of the same job. How many days will 10 men and 8 women together take to complete the same job?
(a) 6
(b) 1312
(c) 12
(d) Data inadequate
(e) None of these
Ans.b

12 M × 18 = 12 W × 18 × 43

\ w = 3/4 M

10M + 8W = 10M + 8 × 34M = 16 M

\16 men can complete the same work

in \(\frac{12 \times 18}{16} = \frac{27}{2} = 13\tfrac{1}{2} \; days\)

2. Seven men and four boys can complete a work in 6 days. A man completes double the work than a boy. In how many days will 5 men and 4 boys complete the work?
(a) 5
(b) 4
(c) 6
(d) Cannot be determined
(e) None of these
Ans.e

M = 2B

∴ 7M + 4B = 14B + 4B = 18B

5M + 4B = 10B + 4B = 14B

∴ 18 boys complete the work in 6 days.

∴ 14 boys complete the work in

\(\frac{6 \times 18}{14} = 7\tfrac{5}{7} \; days\)

Note: 7 men and 4 boys complete the work in 6 days. We have to find out the no. of days in which 5 men and 4 boys complete the work. Here, we see that 4 boys are common in both the cases, therefore, 5 men will take more time to complete the work, i.e., more than 6 days, which is not given in any options. Therefore, without calculating we can say that our answer is(e).

3. The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours. If working 6 hours per day, 9 men can complete a work in 6 days then in how many days can 12 men, 12 women and 12 boys together finish the same work by working 8 hours per day?
(a) 113 days
(b) 323 days
(c) 3 days
(d) 112 days
(e) None of these
Ans.d

8W = 6M = 12B

12M + 12W + 12B Þ 12M + 9M + 6M = 27M

\9 men can complete the work by working 1 hour per day in 6 × 6 days

\27 men working 8 hours per day = \(\frac{6 \times 6 \times 9}{27 \times 8} = 1\tfrac{1}{2} \; days\)

4. Tap ‘A’ can fill a water tank in 25 minutes, tap ‘B’ can fill the same tank in 40 minutes and tap ‘C’ can empty that tank in 30 minutes. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied?
(a) 3213
(b) 15513
(c) 8213
(d) 311119
(e) None of these
Ans.d

Tank filled in 1 minute = 125 + 140 - 130 part

= \(\frac{24 + 15 - 20}{600} = \frac{19}{600}\) part

∴ tank will be filled complete in minutes

= 60019 = 311119

5. Machine A can print one lakh books in 8 hours. Machine B can do the same job in 10 hours. Machine C can do the same job in 12 hours. All the three machines start job at 9.00 am. A breaks down at 11.00 am and the other two machines finish the job. Approximately at what time will the job be finished?
(a) 12.00 noon
(b) 1.30 pm
(c) 1.00 pm
(d) 11.30 am
(e) None of these
Ans.c

Part of print done by A, B and C in 2 hours = 2(18 + 110 + 112) = 3760

Remaining = 1 - 3760 = 2360

If B and C print together, then they can print in \(\frac{10 \times 12}{10 + 12}\)

Therefore, remaining part can be printed by

B and C in \(\frac{10 \times 12}{22} \times \frac{23}{60}\) ≈ 2 hrs.

Hence, the job will be finished at

9 am + 2 + 2 = 1.00 p.m.

6. Suresh can complete a job in 15 hours. Ashutosh alone can complete the same job in 10 hours. Suresh works for 9 hours and then the remaining job is completed by Ashutosh. How many hours will it take Ashutosh to complete the remaining job alone?
(a) 4
(b) 5
(c) 6
(d) 12
(e) None of these
Ans.a

The part of job that Suresh completes in 9 hours

= 915 = 35

Remaining job = 1 - 35 = 25

Remaining job can be done by Ashutosh in 25 × 10 = 4 hours

7. 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many days will a woman finish the work?
(a) 125 days
(b) 150 days
(c) 90 days
(d) 225 days
(e) None of these
Ans.d

15 women's work of a day = 16 - 110115 part

∴ for 1 whole part a woman will take

= 15 × 15 = 225 days.

8. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
(a) 35 hours
(b) 25 hours
(c) 20 hours
(d) Cannot be determined
(e) None of these
Ans.a

Here ratio of efficiencies of pipes A, B and C are as follows:

\(\frac{\begin{matrix} C \;\;\; & B \;\;\; & A\\ 2 \;\;\; & 1 \;\;\; & \\ & 2 \;\;\; & 1 \end{matrix}} {\begin{matrix} 4 & : & 2 & : & 1 \end{matrix}}\)

Suppose the efficiencies of pipes C, B and A are 4K, 2K and K.

Since, the tank is filled in 5 hours by the three pipes having combined efficiency equal to 7K, the time required to fill the tank by A alone = \(\frac{7K \times 5}{K} = 35 \; hours\)

9. 24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is :
(a) 30
(b) 32
(c) 34
(d) 36
(e) None of these
Ans.b

m1 × d1 × t1 × w2 = m2 × d2 × t2 × w1

24 × 10 × 8 × 1 = m2 × 6 × 10 × 1

⇒ m2 = \(\frac{24 \times 10 \times 8}{6 \times 10} = 32 \; men\)

10. A water tank is 25th full. Pipe A can fill the tank in 10 minutes and the pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(a) 6 minutes to empty
(b) 6 minutes to fill
(c) 9 minutes to empty
(d) 9 minutes to fill
(e) None of these
Ans.a

∵ Pipe A in 1 minute fills 110 part and Pipe Bin 1 min.empties 16 part

\ Pipe A + B in 1 min = 110 - 16 = -115

115 part gets emptied in 1 min

\ 25 part is emptied in 15 × 25 min = 6 min.