Applied Numeracy Calculations Flashcards

A startup company's user base grew by 150% in its first year and then by 200% in its second year. What was the total percentage increase in the user base over the two-year period?

Answer: 950%

Let the initial user base be U. After the first year, it grows by 150%, so the new user base is U + 1.5U = 2.5U. In the second year, this new base grows by 200%, so the final user base is 2.5U + 2.0*(2.5U) = 2.5U + 5U = 7.5U. The total increase is 7.5U - U = 6.5U. To express this as a percentage of the original user base U, we calculate (6.5U / U) * 100 = 650%.

A factory has two machines, A and B, that produce widgets. Machine A, working alone, can produce a full batch of widgets in 6 hours. Machine B, working alone, can produce the same batch in 4 hours. If both machines work together, how long will it take them to produce a full batch of widgets?

Answer: 2.4 hours

This is a classic work-rate problem. Machine A's rate is 1/6 of the batch per hour. Machine B's rate is 1/4 of the batch per hour. When working together, their rates add up: (1/6) + (1/4). To add these fractions, find a common denominator, which is 12. So, (2/12) + (3/12) = 5/12 of the batch per hour. To find the total time, take the reciprocal of the combined rate: 1 / (5/12) = 12/5 = 2.4 hours.

A retail company buys a product for $80 and applies a 60% markup to determine the selling price. The company then offers a 25% discount on the selling price during a sale. What is the final sale price of the product?

Answer: $96

First, calculate the initial selling price after the markup. Markup = 60% of $80 = 0.60 * $80 = $48. Selling Price = Cost + Markup = $80 + $48 = $128. Next, calculate the discount. Discount = 25% of $128 = 0.25 * $128 = $32. Final Sale Price = Selling Price - Discount = $128 - $32 = $96.

A project manager is allocating a budget of $500,000. 40% is allocated to Research & Development, 35% to Marketing, and the rest is allocated to Operational Costs. Which of the following statements is true?

Answer: The Operational Costs budget is $125,000.

First, calculate the percentage for Operational Costs: 100% - 40% (R&D) - 35% (Marketing) = 25%. Now calculate the budget for each category: R&D = 0.40 * $500,000 = $200,000. Marketing = 0.35 * $500,000 = $175,000. Operational Costs = 0.25 * $500,000 = $125,000. Evaluating the options: A is false ($175k is $50k more than $125k). B is false ($200k is not double $125k). C is true. D is false ($200k + $175k = $375k, not $425k).

A train travels from City A to City B, a distance of 450 kilometers. The journey takes 5 hours. On the return trip from City B to City A, the train's average speed is 10% faster. How long does the return trip take?

Answer: Approximately 4 hours and 33 minutes

First, calculate the initial speed: Speed = Distance / Time = 450 km / 5 hours = 90 km/h. The return speed is 10% faster: 90 km/h * 1.10 = 99 km/h. Now, calculate the time for the return trip: Time = Distance / Speed = 450 km / 99 km/h ≈ 4.545 hours. To convert the decimal part to minutes: 0.545 hours * 60 minutes/hour ≈ 32.7 minutes, which is approximately 33 minutes. So the return trip takes about 4 hours and 33 minutes.

An investment of €12,000 earns simple interest at a rate of 5% per annum. How much total interest will have been earned after 42 months?

Answer: €2,100

The formula for simple interest is I = P * R * T, where I is interest, P is principal, R is the annual rate, and T is the time in years. First, convert the time from months to years: T = 42 months / 12 months/year = 3.5 years. Now, apply the formula: I = €12,000 * 0.05 * 3.5 = €2,100.