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Given: 10kg of a mixture contains 30% sand and 70% clay.
Asked: 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?

10 kg mixture: -
Sand = 30%*10 = 3 kg
Clay = 70%*10 = 7 kg

In replace mixture: -
Sand = 3 - .3x + x = 3 + .7x
Clay = 7 - .7x = 7 - .7x
Since Sand = Clay
3 + .7x = 7 - .7x
4 = 1.4x
x = 4/1.4 = 40/14 = 20/7

IMO C
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Fastest way is to use alligations, like others have mentioned.

30% 100%
50%

(100-50) (50-30)
50 + 20 =70 parts if the total

Thus proportion that needs to be added is 20/70 = 2/7

To know how many kg is that, we need to multiply by the total 10kg value
2/7 x 10 = 20/7 Answer
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now there are 3 kg of sand out of 10kg and you want them to be 5kg: so 5-3 equal to 2kg
to do that you need to remove x amount with 30% concentration of sand and add x amount with 100% concentration of sand

2kg = -30%x+100%x
2kg = 70%x
x=20/7

you can also do it on clay side:
now there are 7 kg of clay out of 10kg and you want them to be 5kg: so 5-7 equal to -2kg
-2kg=-70%x
x=20/7
in words: how much of something that is 70% I need to remove to subtract 2kg?­
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Easiest Method:
When Sand and Clay would be equal it would be 5 Kg each. Apply formula for clay:
Final Quantity = Initial quantity(1 - x/C) x-> Replacing amount; C is total Capacity

5 = 7(1 - x/10).
x= 20/7
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KarishmaB ma'am can you please tell me where am I going wrong using allegations ?
A = mixture quantity
B = pure sand quantity
30 -- 50 -- 100%
A- ---- B
so 20(A) = 50(B)
so A/B= 5/2 now A = 10kg given so B = 4 so 4 kgs of pure sand was added hence 4kgs must also have been removed initially ??
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djangobackend
KarishmaB ma'am can you please tell me where am I going wrong using allegations ?
A = mixture quantity
B = pure sand quantity
30 -- 50 -- 100%
A- ---- B
so 20(A) = 50(B)
so A/B= 5/2 now A = 10kg given so B = 4 so 4 kgs of pure sand was added hence 4kgs must also have been removed initially ??

If we were to mix pure sand with 10 kg of mixture, then your answer would be correct. But that is not what we are supposed to do. We must remove some mixture and then mix pure sand.
All we know is that they need to be in the ratio 5:2 finally.
Hence total mixture would be 7 parts which is actually equal to 10 kg. Out of this 2/7th would be pure sand i.e. 20/7 kg would be pure sand.

Check the first part of this blog post: https://anaprep.com/arithmetic-replacement-in-mixtures/
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