Choose the two true statements from the following.
Options
A) If the rate of inflation as measured by the RPI is 2%, then a pension index linked to the RPI will increase by 2%.
B) A price ratio of 0.8 corresponds to a price decrease of 80%.
C) If the price of transport rises by 10% in a year, then the value of the RPI must rise by 10%.
D) In a particular job, the earnings ratio at the mean of women’s earnings to men’s earnings is 90%, so women earn 10% more than men doing the same job at the mean.
E) If the price of an air ticket decreases from £75 to £70, then the price has decreased by 5%.
F) A steam engine 12.6m long has wheels of circumference 3.1m. A scale model of the steam engine 21 cm long will have wheels of circumference 4.7 cm.
G) A plumber’s bill is £124 before VAT (at 17.5%) is added. The total bill including VAT is £145.70
A is true
G 124* 1.175 = 145.7 sure enough
naughty naughty OU assignments!
The two true statements from the options provided are:
B) A price ratio of 0.8 corresponds to a price decrease of 80%.
G) A plumber’s bill is £124 before VAT (at 17.5%) is added. The total bill including VAT is £145.70.
Explanation:
To determine the true statements, let's go through the options one by one:
A) If the rate of inflation as measured by the RPI is 2%, then a pension index linked to the RPI will increase by 2%.
This statement is false. The rate of inflation and the increase in a pension index linked to the RPI may not necessarily be the same. Other factors can influence the pension index increase, such as different formulas or adjustments.
B) A price ratio of 0.8 corresponds to a price decrease of 80%.
This statement is true. To calculate the percentage decrease from a price ratio, subtract the ratio from 1 and multiply by 100. Here, 1 - 0.8 = 0.2, and 0.2 multiplied by 100 results in 20%. Therefore, the price decrease is 20%.
C) If the price of transport rises by 10% in a year, then the value of the RPI must rise by 10%.
This statement is false. The RPI (Retail Price Index) measures the average change in prices for a basket of goods and services, including transportation but not limited to it. Therefore, a 10% rise in the price of transport does not imply a corresponding 10% rise in the RPI.
D) In a particular job, the earnings ratio at the mean of women’s earnings to men’s earnings is 90%, so women earn 10% more than men doing the same job at the mean.
This statement is false. An earnings ratio of 90% means that women earn 90% of what men earn, not 10% more. If women earned 10% more than men, the earnings ratio would be 110%.
E) If the price of an air ticket decreases from £75 to £70, then the price has decreased by 5%.
This statement is false. To calculate the percentage decrease, divide the difference between the new price and the old price by the old price and multiply by 100. In this case, (75 - 70) / 75 multiplied by 100 results in approximately 6.67%. Therefore, the price has decreased by approximately 6.67%, not 5%.
F) A steam engine 12.6m long has wheels of circumference 3.1m. A scale model of the steam engine 21 cm long will have wheels of circumference 4.7 cm.
This statement is false. Since the scale of the model is 21 cm/12.6 m, or 0.167, the circumference of the model's wheels should be 3.1 m * 0.167 = 0.5177 m, not 4.7 cm.
G) A plumber’s bill is £124 before VAT (at 17.5%) is added. The total bill including VAT is £145.70.
This statement is true. To find the bill including VAT, add the VAT amount to the original bill. The VAT amount is calculated by multiplying the original bill (£124) by the VAT rate (17.5%) and dividing by 100. Therefore, £124 * (17.5/100) = £21.70. Adding this VAT amount to the original bill (£124 + £21.70) gives a total bill of £145.70.