A homeowner has installed two systems of gutters and 100-liter barrels

Question

A homeowner has installed two systems of gutters and 100-liter barrels to collect water that runs off of her roof, one system on the north side and the other on the south side. Sixty percent of the water that falls on her roof runs into the gutters of the north side system and the remaining 40 percent runs into the south side gutters. All water then drains into the barrels. No barrel is attached to both of the gutter systems, and all barrels contain only water that has drained from the gutters.

Suppose that all of the barrels take in water at the same rate and over the same period of time. Select for North side and South side numbers of barrels that are jointly consistent with this supposition and the given information. Make only two selections, one in each column.

Apt0810 · Accepted Answer

Both barrels have 100litres capacity,and north takes 60% of total water falling,while south takes 40% of the total ,so

x=No.of barrels which need to be placed in line to collect the total water in north side.
y=No.of barrels which need to be placed in line to collect the total water in south side.

0.6*T=100*x
0.4*T=100*y

So now here T would be an integer,so x should be something which is divisble by 6 and y should be something which is divisble by 4,so per the options

The best possible value of x is 6 and y is 4

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PhlpSrks · Answer

Well,

The ratio is   (0.6):(0.4)  .

As there is no fractional barrel, we must multiply this ratio until we reach integers.

Multiplying by  (x5)  we would reach  3:2 , but there is no such option.

The next integer show up up if we multiply the ratio by  (x10) , which yields  6:4 .

AdarshSambare · Answer

Hey  Bunuel 
Got the answer but need clarification.
Only 100-liter barrels can be used.
North side collect 60%
South side collect 40%
Let's assume 100 liters of water so water collected: 
==> N:S = 60:40
I cannot find anything in the question which says the tank cannot be fractional
Multiplying them with X 5
==> N:S = 300:200
Tanks needed is 3:2
since there no 2 in South side
Multiplying them with X 2
 ==> 6:4 
Select the Answer

Bunuel · Answer

Barrels must be whole numbers. 3:2 matches the ratio, but “2” isn’t an option. Scale up to 6:4, which is valid.

tryorcry · Answer

Question was simple and the ratio of water in this case that should be drained from northside of the roof to south side must be 6:4

but mathematically, 
let rate of water inflow to barrels be x/hour .
volume of each barrel in y hours be x*y

this will be same for all barrels in y hours.

let the total volume be W

so as per question , in north side , 60% of W = volume of each barrel * no of barrels in north (N)
i.e, 0.6W= (x*y)*N
and for south, 
0.4W= (x*y)*S

dividing both 
6/4 = N/S

S*6=N*4

hence , no. of barrels in north = 6 and in south = 4

A homeowner has installed two systems of gutters and 100-liter barrels

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A homeowner has installed two systems of gutters and 100-liter barrels

Prep Toolkit

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