Percent problems and financial mathematics

2010008304

Level: 
A
At the beginning of the therapy, three monitored patients were of the same weight. Their weights were changing as follows: (a) Patient A gained \(6\%\) of his weight and then his weight did not change. (b) Patient B lost \(2\%\) of his weight first, but later he gained \(8\%\) of his weight. (c) Patient C gained \(2\%\) of his weight and later he gained another \(4\%\) of his weight. Which patient has the lowest weight after the therapy?
Patient B
Patient A
Patient C
After described weight changes everyone will weigh the same.

2010008303

Level: 
A
Three merchants were selling the same product for the same price. Successively they adjusted the prices as follows: (a) Merchant A first increased the price of the product by \(5\%\), but later reduced it by \(10\%\). (b) Merchant B first reduced the price of the product by \(2\%\) and later reduced it again, this time by \(3\%\). (c) Merchant C adjusted the price of the product only once. He cheapened the product by \(10\%\). Which merchant offers the product for the highest price after price adjustments?
Merchant B
Merchant A
Merchant C
All merchants will sell the product for the same price.

2010008302

Level: 
A
During epidemic the towns reported the ratios of ill citizens (see the table). Which town had the biggest number of ill citizens on 1$^{\mathrm{st}}$ July (*). \[\begin{array}{|c|c|c|} \hline \text{Town} & \text{Total population} & \text{Ratio of ill citizens on *} \\\hline A & 8\,000 & 4.0\% \\\hline B & 64\,000 & 0.5\% \\\hline C & 320\,000 & 0.1\% \\\hline \end{array}\]
All towns had the same number of ill citizens.
The biggest number of ill citizens was in the town A.
The biggest number of ill citizens was in the town B.
The biggest number of ill citizens was in the town C.

2010008301

Level: 
A
Three companies made a commitment to donate a portion of their annual profit to charity (see the table). Which company did donate the biggest sum? \[\begin{array}{|c|c|c|} \hline \text{Company} & \text{Annual profit} & \text{Ratio from annual profit} \\\hline A & 6\,000\,000 & 4.0\% \\\hline B & 12\,000\,000 & 2.0\% \\\hline C & 48\,000\,000 & 0.5\% \\\hline \end{array}\]
All companies donated the same sum.
The biggest donor was the company A.
The biggest donor was the company B.
The biggest donor was the company C.

2010006402

Level: 
C
One third of a number \( a \) is by \( 75\% \) greater than one seventh of a number \( b \). Choose the true statement.
The number \(a\) is by \(25\%\) smaller than \(b\).
The number \(a\) is by \(75\%\) smaller than \(b\).
The number \(a\) is by \(400\%\) greater than \(b\).
The number \(a\) is by \(75\%\) greater than \(b\).

2010006209

Level: 
B
The angle \( \beta \) is by \( 20\% \) smaller than the angle \( \gamma \) and by \( 100\% \) greater than the angle \( \alpha \). The angle \( \alpha \) is
by \( 60\% \) smaller than \( \gamma \).
by \( 40\% \) smaller than \( \gamma \).
by \( 20\% \) smaller than \( \gamma \).
by \( 80\% \) smaller than \( \gamma \).

2010006208

Level: 
B
There are \(14\) right-handed and \(18\) left-handed children among the children attending the ceramic group. Find the difference between percentages of right-handers and left-handers in the group. (Round the result to one decimal place.)
differ by \(27.3\, \%\)
differ by \(63.6\, \%\)
differ by \(36.4\, \%\)
differ by \(57.1\, \%\)