Time and Work: Quiz

Directions: Study the following information and answer the questions given below:

1. 2 men or 5 women or 7 boys can finish a work in 469 days, then the number of days taken by  7 men, 5 women and 2 boys to finish the work is-

1. 134
2. 106
3. 100
4. 98

2.  6 children and 2 men complete a certain piece of work in 6 days. Each child takes twice the time taken by a man to finish the work. In how many days will 5 men finish the same work-?

1. 6
2. 8
3. 9
4. 15

3.(x-2) men can do a piece of work in x days and (x+7) men can do 75%of the same work in (x-10) days. Then in how many days can (x+10) men finish the work?

1. 27
2. 12
3. 25
4. 18

4.  A man , a woman and a girl worked for a contractor for the same period. A man is twice efficient as a woman and a woman is thrice efficient as girl Rs. 10000 were given to all of them. What is the sum of money received by a woman and a girl together?

1. 5500/-
2. 4500/-
3. 4000/-
4. 6000/-

5.A piece of work can be done by 10 men and 6 women in 18 days. Men work 9 hr per day while women work 7.5 hr per day. Per hr efficiency of a woman is 2/3 of a man’s. In how many days 10 men and 9 women complete the work?

1. 16
2. 20
3. 30
4. 25

6.Tap A can fill a tank in 20 hr, B in 25 hr but tap C can empty a full tank in 30 hr. Starting with A, followed by B and C each tap opens alternatively for one hr period till the tank gets filled up completely. In how many hr the tank will be filled up completely?

1. 51 11/15
2. 52 2/3
3. 24 4/11
4. None of these

7. If one pipe A can fill a tank in 20 min, then 5 pipes, each of 20%efficiency of A, can fill the tank in-

1. 80 min
2. 100 min
3. 20 min
4. 25 min

8. A, B and C three weavers have to supply an order of 100 Sweater. A can weave a Sweater in 2 hr, B in 3 hr and C in 4 hr respectively. It is known that even being a joint contract each one weaver help to the rest weavers. In how many hr they will complete the order irrespective of day or night?

1. 93 hr
2. 100 hr
3. 92 4/13 hr
4. 94 hr

9. A tank is connected with 4 pipes A, B, C and D of which two are filling the tank and other two are emptying it. The time taken by A, B, C and D to finish their jobs are 10hr, 15hr, 20 hr and 30 hr respectively. All four pipes are opened. When the tank was empty, it took 12 hr to fill it completely. Which two are the outlet pipes?

1. A and B
2. C and D
3. A and C
4. B and D

10.Himesh and fatima are two different persons, but when they worked together they complete it in 10 days. Had Himesh worked at half of his efficiency and Fatima at five times of his efficiency it would have taken them to finish the job in 50% of the scheduled time. In how many days Fatima can complete the job working alone?

1. 15 days
2. 24 days
3. 15 days
4. 30 days

SOLUTION

1. 2 men = 7 boys => 1man= 7/2 days

5 women= 7boys=> 1 women=7/5boys

7men+5women+2boys=7×7/2+5×7/5+2=67/2boys

Now,     B1*D1= B2*D2

 7*469=67/2*D2

D2= 98days

2. 6C+2M=6days

36C+12M=1days

Again

1M=2C

36+12*2=1day

60 children can do the work in 1day

Now, 5men= 10Children

10 children can do the work in 6days.

3. ¾*(x-2)x=(x+7)(x-10)

X­­­­­­­2 – 6x-280=0

X=20 and x= -14

So, the acceptable value is x=20

Total work= (x-2)*x=18*20=360unit

Now       360=30*K         (30=20+10)

K=12days

4. Efficiency of a man :  woman   : girl  = 6:3:1

Share of a woman and girl =   (3+1)/(6+3+1)*10000

=4/10*10000=Rs.4000

5. Work of a man for 1 hour= 3/2 women’s work for 1 hour

Again, work of a man for 1 da   =(3/2*9/7.5)women’s  work for 1 hour

Work of a man for 1 day= 9/5 women’s work for 1 day

1man=9/5women

10Men+6Women= 10* 9/5 + 6=24women

10Men+9 Women= 10*9/5 + 9= 27 women

Now,

D1*W1= D2*W2

                                                    18*24= D2*27

D2= 16 days

6. Efficiency of A=5%

Efficiency of B=4%

Efficiency of C= -3.33%

It means in every 3 consecutive hours taps A,B and C can fil    5.66% =(5+4-3.33)

Therefore in 51 hours= (3*17) taps A,B and C can fill 96.33%=(5.66*17)

The remaining part i.e, 3.66%=(100-96.33) can be filled up by A in 11/15 hours =(3.66/5),sine it is now A’s turn

Hence the total time required= 51+11/15=51 11/15

7. 20 minute

8. LCM of 2,3 and 4= 12

In 12 hours A will make 6 Sweter

In 12 hours B will make 4 Sweter

In 12 hours C will make 3 Sweter

i.e, in 12 hours they will weave 13 sweter

so, in 84 hours they will weave 91 sweter

Now, in 9 hours A will make 4 sweter

In 9 hours B will make 3 sweter

In 9 hours C will make 2 sweter

So. They will complete 100 sweter in 93 hours.

Note: Since, they cannot share each others work so B will take completely 9 hours to make 3 sweter,even when A and C stay idle for the last 1 hour till B completes his own work.

9. Efficiency of A=10%

Efficiency of B= 6.66%

Efficiency of C= 5%

Efficiency of D= 3.33%

Efficiency of A+B+C+D=8.33     (TIME=12HOURS)

Now, go through options and consider A and B as inlet pipes and C and D as outlet pipes, then

(10+6.66)-(5+3.33)=8.33

Which is required hence it is certain that C and D are outlet pipes.

10. Efficiency of Himesh and Fatima (Combined)=10%

Consider option (d)

Efficiency of Fatima=3.33%

Efficiency of Himesh=6.66%

Now, the new efficiency of Fatima=16.66%

And the new efficiency of Himesh = 3.33%

Therefore, newly combined efficiency of Himesh and Fatima=20%

Therefore, required number of days by Himesh and Fatima

Working together=5

Since 5 is half of 10, hence the option (D) is correct.