Percentage: Level 4
1.
A library has 200 books, 30% of which are non-fiction. The library receives a donation of 300 new books. After the donation, 40% of the total collection is non-fiction. What percent of the **newly donated** books are non-fiction?
Solution (C):
1. Original: 200 books. Non-fiction = \(30\% \text{ of } 200 = 60\).
2. New Total: \(200 + 300 = 500\) books.
3. Final Non-fiction: \(40\% \text{ of } 500 = 200\).
4. Donated Non-fiction: Total Final – Original = \(200 – 60 = 140\).
5. Percent of Donation: The donation was 300 books.
\( \frac{140}{300} = \frac{14}{30} = \frac{7}{15} \approx 46.66\% \).
2.
A store marked up a shirt by 25% above its cost price. Later, during a sale, the store offered a discount of 20% off the marked price. If the shirt sold for $60, what was the original cost price?
Solution (B):
Let Cost Price = \(C\).
1. Marked Price \(M = 1.25C\).
2. Sale Price = \(M \times (1 – 0.20) = 0.80M\).
3. Substitute M: Sale Price = \(0.80(1.25C) = 1C = C\).
4. Since the Sale Price is $60, the Cost Price \(C\) is also $60.
(A 25% increase followed by a 20% decrease returns to the original value because \( \frac{5}{4} \times \frac{4}{5} = 1 \)).
3.
In an election between two candidates, Candidate A received 60% of the total votes. If 20% of the total votes were declared invalid, and the total number of votes cast was 5,000, how many **valid** votes did Candidate B receive? (Assume the 60% refers to the total votes cast, not just valid ones).
Solution (D):
Wait, let’s re-read carefully. Usually, vote percentages are based on valid votes, but the prompt says “A received 60% of the total votes”. Let’s assume standard distribution of remaining votes.
1. Total Votes = 5000.
2. Invalid Votes = \(20\% \text{ of } 5000 = 1000\).
3. Valid Votes = \(5000 – 1000 = 4000\).
4. If Candidate A got 60% of the total votes (as stated), A got \(0.60 \times 5000 = 3000\) votes.
5. Since there are only 4000 valid votes, and A took 3000 of them, Candidate B must have received the remaining valid votes.
6. \(B = \text{Valid} – A = 4000 – 3000 = 1000\).
Score: 0 / 0