Percent problems

2010018204

Level: 
B
The aluminium rod and brass rod have the same length at a given temperature. The material constants of the rods are: αaluminium=24⋅10−6K−1 and αbrass=18⋅10−6K−1. Suppose both rods are heated to the same higher temperature. Find the true statement about the extensions of both rods. Round the percentage difference in the rods’ extensions to the whole percent.   Hint: Solid materials expand upon heating. The rod with the initial length l0 is upon the temperature increasing by Δt extended by the value Δl=l0⋅α⋅Δt, where α is the material constant (coefficient of linear thermal expansion) that is indicative of the extent to which a material expands upon heating.
The extension of the aluminium rod is by 33% greater than the extension of the brass rod.
The extension of the aluminium rod is by 67% greater than the extension of the brass rod.
The extension of the aluminium rod is by 133% greater than the extension of the brass rod.
The extension of the aluminium rod is by 33% less than the extension of the brass rod.

2010018203

Level: 
B
A protective layer of thickness d reduces the level of harmful radiation by 10%. Determine what is the percentage decrease in the original level of harmful radiation after passing through the layer of thickness 3d. Round the result to the whole percent.
73%
70%
30%
27%

2000016301

Level: 
C
Investors Thomas and Paul invested the same amount. After the first year, the value of Thomas's investments decreased by 5o/o, but after the following year, their value increased by 5o/o. Paul's investments were more stable. After the first year, the value of his investments increased by 2o/oo, but after the second year, it decreased again by 2o/oo. Determine the true statement about the value of Thomas and Paul's investments two years after the investment.
Paul's investments will have a higher value.
Thomas's investments will have a higher value.
The values of both investments will again be the same.
It is not possible to determine the ratio of the values of Paul and Thomas's investments from the given data.

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 1st July. TownTotal populationRatio of ill citizens on 1st July 2020A80004.0%B640000.5%C3200000.1%
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? CompanyAnnual profitRatio from annual profitA60000004.0%B120000002.0%C480000000.5%
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.