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QuestionA tank is 23\frac{2}{3} full at 2400 Litres. Find Litres when half-full and the percentage needed to fill it.

Studdy Solution

STEP 1

Assumptions1. The tank is 3\frac{}{3} full and this is equivalent to2400 Litres. . Peter claims that the total capacity of the tank is3600 Litres.
3. We need to find the volume of water when the tank is half full.
4. We also need to find the percentage of water needed to fill up the tank.

STEP 2

First, let's verify Peter's claim. If the tank is 2\frac{2}{} full and this is equivalent to2400 Litres, then the total capacity of the tank can be found by dividing the current volume by 2\frac{2}{}.
Total capacity=Current volume/2Total\, capacity = Current\, volume / \frac{2}{}

STEP 3

Now, plug in the given values for the current volume to calculate the total capacity.
Total capacity=2400 Litres/23Total\, capacity =2400\, Litres / \frac{2}{3}

STEP 4

Calculate the total capacity of the tank.
Total capacity=2400 Litres/23=3600 LitresTotal\, capacity =2400\, Litres / \frac{2}{3} =3600\, LitresPeter's claim is correct.

STEP 5

Now, let's find the volume of water when the tank is half full. This can be found by multiplying the total capacity by 12\frac{1}{2}.
Half full volume=Total capacitytimes12Half\, full\, volume = Total\, capacity \\times \frac{1}{2}

STEP 6

Plug in the values for the total capacity to calculate the half full volume.
Half full volume=3600 Litrestimes12Half\, full\, volume =3600\, Litres \\times \frac{1}{2}

STEP 7

Calculate the half full volume.
Half full volume=3600 Litrestimes12=1800 LitresHalf\, full\, volume =3600\, Litres \\times \frac{1}{2} =1800\, LitresWhen the tank is half full, it contains1800 Litres of water.

STEP 8

Finally, let's find the percentage of water needed to fill up the tank. This can be found by subtracting the current volume from the total capacity, dividing by the total capacity, and then multiplying by100.
Percentage needed=(Total capacity−Current volumeTotal capacity)times100Percentage\, needed = \left(\frac{Total\, capacity - Current\, volume}{Total\, capacity}\right) \\times100

STEP 9

Plug in the values for the total capacity and the current volume to calculate the percentage needed.
Percentage needed=(360 Litres−240 Litres360 Litres)times100Percentage\, needed = \left(\frac{360\, Litres -240\, Litres}{360\, Litres}\right) \\times100

STEP 10

Calculate the percentage needed.
Percentage needed=(1200 Litres3600 Litres)times100=33.33%Percentage\, needed = \left(\frac{1200\, Litres}{3600\, Litres}\right) \\times100 =33.33\%

STEP 11

Round off the answer to the nearest percentage.
Percentage needed=33%Percentage\, needed =33\%To fill up the water tank,33% more water is needed.

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