davesinger786 wrote:
Quote:
10kg of a mixture contains 30% sand and 70% clay. In order to make the mixture contain equal quantities of clay and sand how much of the mixture is to be removed and replaced with pure sand?.
Hi Economist,
The amount in that table will be total amount ? If we're considering "Sand" then why not use the amount of Sand in the mixture which is 3 kg in this case? Please give some idea.Thanks
Don't ever try to find a Easier/Shortcut way unless you are clear about the basic methodThe basic method goes like this (Making an equation and solving it further)
Let, x is the amount of mixture to be replaced with Pure Sand. The please understand that since we are replacing Mixture with sand so
1) the amount of Sand that goes out with x kg Mixture will come back with the pure sand
2) the amount of Clay that goes out with x kg Mixture will be replaced by pure sand
i.e. Total Amount of Sand will increase by the amount of clay that is removed while removing x kg of mixture
Please know that Sand in the mixture as of now = (30/100)*10 = 3 kg.
Clay as of now = 10 - 3 = 7kg
Clay that goes out in x kg of mixture = (70/100)*x = (7x/10) kg.
METHOD-1Then Total Sand after the mixture is replaced with pure sand = 3+ (7x/10) kg.
But now Sand and Clay should be equal in the final mixture
i.e. Sand = 50% of total Mixture amount
i.e. 3+ (7x/10) = (50/100)*10
i.e. 3+ (7x/10) = 5
i.e. (7x/10) = 2
i.e. x = 20/7 kgMETHOD-2Same equations can also be made on the quantity of clay after the x kg Mixture is replaced with x kg pure Sand
i.e. Clay that goes out in x kg of mixture = (70/100)*x = (7x/10) kg.
i.e. Clay after the Mixture is Replaced with Pure Sand = 7 - (7x/10) kg.
But now Sand and Clay should be equal in the final mixture
i.e. Clay = 50% of total Mixture amount
i.e. 7 - (7x/10) = (50/100)*10
i.e. 7 - (7x/10) = 5
i.e. (7x/10) = 2
i.e. x = 20/7 kgI hope it helps!
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