Arithmetic+ 03: UNIZOR.COM - Math+ & Problems - Arithmetic
Channel: Zor Shekhtman on UNIZOR Education
Date: 2024-01-17

UNIZOR.COM - Creative Mind through Art of Mathematics
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Arithmetic+ 03


Problem A

I have purchased a share of some company XYZ for price P0=$100.
After a month the price was lower by ρ=10%.
Another month later the price went up by the same percentage ρ=10% and I sold this share.
Have I lost or gain money, or got even?

Problem B

I have purchased a share of some company XYZ for price P0=$100.
After a month the price was higher by ρ=10%.
Another month later the price went down by the same percentage ρ=10% and I sold this share.
Have I lost or gain money, or got even?

Problem C

(a) Within the framework of Problems A, what the percentage of gain would neutralize the loss after price moving down by ρ=10%?

(b) Within the framework of Problems B, what the percentage of loss would neutralize the gain after price moving up by ρ=10%?

Problem D (suggested by Max)

Concentration of salt dissolved in water is measured in percentage of the mass of salt to the total mass of solution (salt + water).

Initially, a glass contained 100 gram of solution of salt in water with the concentration of salt 1%.
Question 1: how much salt and how much water was in a glass?

This same glass was standing on a table for a week and part of water has evaporated, so the concentration of salt after a week became 2%.
Question 2: how much salt and how much water was in a glass after this process of evaporation?
Question 3: how much water has evaporated in a week?