HCL Time and Works and Pipes and Cisterns Quiz-1

Together they can complete in = (12 x 8)/(12 + 8) = 96/20 = 4.8 ~ 5 days

Together they can complete the project in 6 days.

Shruti can complete the project in 8 days

So, Ankita can complete the project in = LCM of days / Difference between LCM

                                                              = 24/(4-3) 

                                                              = 24 days

Avik and Vibudh 1 hour work = 1/12

Anjali and Vibudh 1 hour work = 1/15

Avik and Anjali 1 hour work = 1/20

Avik, Vibudh, Anjali’s 1 hour work = \frac{1}{2}(\frac{1}{12} +\frac{1}{15} +\frac{1}{20} = 1/10

So, Avik, Vibudh, Anjali together can do the painting in 10 hours.

One day work by Suvam : One day work by Sayan = 3:1

(Suvam + Sayan)it's one-day work = 1/18

Now, when we divide 1/18 in the ratio of 3:1

Therefore, Suvam’s one day work = (1/18) x (3/4) = 1/24

Hence, Suvam can finish it alone in 24 days.

Mansih and Ashish 5 days’ work = 5(1/25 + 1/20) = 9/20

Work left= 1 – 9/20 = 11/20

Now, 1/20 work is finished by Asish in 1 day.

Therefore, 11/20 work will be finished by Asish in 11 days

Sahil can finish in 7 days

Arpan can finish in 4 days

Together they can finish in = (7 x 4)/(7-4) = 28/3 = 9.3 ~ 10 days

Total capacity of cistern = 40*13 = 520 liters

 

Total vessels needed to fill the cistern if the total volume of each vessel is reduces to 20 liters = 40*13 / 20 = 520/10 = 52 vessels

Pipe ‘M’ can empty in 9 hours

Pipe ‘N’ can empty in 12 hours

So, they can empty together in = (12 x 9)/(12+9) = 36/7

The complete tank is filled in 7 hours, so in 1 hour = 1/7th tank will be filled

Due to outlet pipe in 1 hour = 1/10th part will be filled

Part of the tank emptied in 1 hour = 1/7 – 1/10 = 3/70

Therefore the tank will be emptied in 70/3  hours

20 km = 20*1000 = 20000 m

 

In 1 hour the level of the water will be = 0.3\times 0.2\times 20,000 = 1200 m^3

 

Let us assume that, in ‘H’ hours the water level will reach to 6m.

Also, in ‘H’ hours the water level will be 1200H.

Therefore, 1200H = 140 × 40 × 6

 => H = (140 × 40 × 6)/1200 = 28