Maths percentage

1. A man bought a number of articles for $400; 2 of them were broken. He then sold the rest at 30% above the cost price and made a profit of $68. How many articles did he buy?

Let the articles he bought be x

the cost price per one article =$(400/x)

the income among all of them=(x-2)(1+30%)(400/x)=$[520(x-2)/x]

As he made a profit of $68,

[520(x-2)/x]-400=68

520(x-2)=468x

52x=1040

x=20

Therefore, he bought 20 articles

2. 3.6 liters of a liquid containing 40% of alcohol. How much water would be added to obtain a liquid containing 30% alcohol?
the volume of alcohol=3.6(40%)=3.6(0.4)=1.44L

Assume xL water has to be added to obtain a liquid containing 30% alcohol

[(1.44)/(3.6+x)]*100%=30%

1.44=0.3(3.6+x)

1.44=1.08+0.3x

0.3x=0.36

x=1.2


Therefore,1.2L water has to be added to obtain a liquid containing 30% alcohol

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