Percentage: Level 2
1.
If 150 is increased by 60% and then decreased by \(y\) percent, the result is 192. What is \(y\)?
Solution (C):
1. First increase: \( 150 \times 1.60 = 240 \).
2. The number becomes 240. Now it decreases to 192.
3. Decrease amount = \( 240 – 192 = 48 \).
4. Percent decrease \( y = \frac{48}{240} \times 100\% = \frac{1}{5} \times 100\% = 20\% \).
2.
A 30% discount reduces the price of a commodity by $90. If the discount is reduced to 20%, what will be the price of the commodity?
Solution (B):
1. Find original price \(P\): \( 30\% \text{ of } P = 90 \implies 0.3P = 90 \implies P = 300 \).
2. New discount is 20%: \( 20\% \text{ of } 300 = 60 \).
3. New Price = \( 300 – 60 = 240 \).
3.
J.R. weighed 200 pounds. He lost 15% of his weight, then gained 35 pounds. What is the net percent change in his weight?
Solution (E):
1. Lost 15%: \( 200 \times 0.85 = 170 \) lbs.
2. Gained 35 lbs: \( 170 + 35 = 205 \) lbs.
3. Change from 200 to 205 is +5 lbs.
4. Percent change = \( \frac{5}{200} \times 100\% = 2.5\% \).
4.
In a class of 200 students, 40% are girls. 25% of the boys and 10% of the girls signed up for a tour. What percent of the **class** signed up?
Solution (A):
1. Girls: \( 40\% \text{ of } 200 = 80 \). Boys: \( 200 – 80 = 120 \).
2. Boys signed up: \( 25\% \text{ of } 120 = 30 \).
3. Girls signed up: \( 10\% \text{ of } 80 = 8 \).
4. Total signed up = \( 30 + 8 = 38 \).
5. Percent of class = \( \frac{38}{200} \times 100\% = 19\% \).
5.
A number that is 50% greater than 60 is what percent less than a number that is 20% less than 150?
Solution (D):
1. Number A: \( 60 + (0.5 \times 60) = 90 \).
2. Number B: \( 150 – (0.2 \times 150) = 150 – 30 = 120 \).
3. We compare A (90) to B (120). How much percent *less* is 90 than 120?
4. Difference = 30. Percent less = \( \frac{30}{120} \times 100\% = 25\% \).
6.
Aloysius spends 50% of his income on rent and 20% on food. He spends 30% of the **remainder** on video games. What percent of his income is left?
Solution (C):
1. Spent initially: \( 50\% + 20\% = 70\% \).
2. Remainder: \( 100\% – 70\% = 30\% \).
3. Video games: \( 30\% \text{ of } 30\% = 0.3 \times 30 = 9\% \) of total income.
4. Total spent: \( 70\% + 9\% = 79\% \).
5. Left: \( 100\% – 79\% = 21\% \).
7.
If the price of a stock increases by 10% one day and decreases by 10% the next day, the final price is:
Solution (B):
Let price = 100.
Day 1: \( 100 + 10 = 110 \).
Day 2: Decrease 110 by 10%. \( 10\% \text{ of } 110 = 11 \).
Final: \( 110 – 11 = 99 \).
This is 1% less than 100.
8.
If \(x\) is 25% of \(y\), what percent of \(x\) is \(y\)?
Solution (A):
\( x = 0.25y \implies x = \frac{1}{4}y \implies y = 4x \).
\( y = 400\% \text{ of } x \).
9.
A population of 500 increases by 20% in the first year and by 25% in the second year. What is the population after two years?
Solution (D):
Year 1: \( 500 \times 1.20 = 600 \).
Year 2: \( 600 \times 1.25 \).
\( 25\% \text{ of } 600 = 150 \).
Total = \( 600 + 150 = 750 \).
10.
If 60% of a number is 12 more than 40% of the same number, what is the number?
Solution (E):
\( 0.6x = 0.4x + 12 \).
\( 0.2x = 12 \).
\( x = \frac{12}{0.2} = 60 \).
Score: 0 / 0