← Back to 3. Mathematical Models in Algebra

📝 Find percent increase (14 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 14 questions available

←Previous Topic:Finding the Whole Given a Part and Percent📝 Find percent increaseFind percent decrease:Next Topic→

What is Find percent increase?

Definition:
Percent increase measures the relative growth from an original amount to a new, larger amount. The formula is $\text{Percent Increase} = \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \times 100\%$ . It quantifies how much a quantity has grown.

Working:
If a price rises from $50 to$ 65, the increase is $65 - 50 = 15$ . Percent increase = $(15/50) \times 100 = 30\%$ .

Example:
Problem: 'A population grew from 200 to 250. Find the percent increase.' Increase = 50, so $(50/200) \times 100 = 25\%$ .

Reason:
Percent increase is widely used in economics, population studies, and business to track growth rates.

Easy

Medium

Hard

📝 All Find percent increase MCQs

Q1. A quantity changes from 80 to 100. Which expression correctly represents the percent increase?

20/100\times100\%

20/80\times100\%

✅

80/100\times100\%

100/20\times100\%

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Percent increase compares the change with the original amount, not the final amount. The change is $100-80=20$ , and dividing by the original $80$ gives $20/80=0.25$ , or $25\%$ .

Q2. A town's population rises from 24,000 to 30,000. A student says the increase is $20\%$ because $6,000$ is $20\%$ of $30,000$ . What is the correct interpretation?

A.The increase is

15\%

B.The increase is

20\%

C.The increase is

25\%

✅

D.The increase is

30\%

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The absolute increase is $30,000-24,000=6,000$ . Percent increase must use the original population as the reference, so $6,000/24,000\times100\%=25\%$ , not $20\%$ .

Q3. A monthly electricity bill increases from Rs. 4,500 to Rs. 5,175. Before calculating, which estimate best predicts the percent increase?

A.About

5\%

B.About

10\%

C.About

15\%

✅

D.About

25\%

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The increase is Rs. $675$ . Since $675$ is approximately $15\%$ of Rs. $4,500$ , the exact percent increase is $675/4500\times100\%=15\%$ . Estimation therefore supports the result.

Q4. A machine originally produces 160 units per hour. After an adjustment, it produces 200 units per hour. Which statement best explains the percentage change?

A.Production increased by

20\%

because 40 is

20\%

of 200.

B.Production increased by

25\%

because 40 is

25\%

of 160. ✅

C.Production increased by

40\%

because the output rose by 40 units.

D.Production increased by

125\%

because 200 is

125\%

of 160.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The output change is $200-160=40$ units. Because percentage increase is measured relative to the original output, calculate $40/160\times100\%=25\%$ . The final output being $125\%$ of the original does not mean the increase is $125\%$ .

Q5. A store raises the price of a backpack from Rs. 2,400 to Rs. 2,760. The manager wants the percentage increase for a report. What should be reported?

12\%

15\%

✅

18\%

20\%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The price increase is Rs. $360$ . Dividing the change by the original price gives $360/2400=0.15$ . Multiplying by $100\%$ gives a $15\%$ increase. Using the final price as the denominator would produce a misleading percentage.

Q6. A company's online orders rise from 1,200 in January to 1,500 in February and then to 1,800 in March. Which statement correctly compares the two monthly percent increases?

A.Both increases are

25\%

B.January-to-February is

25\%

, while February-to-March is

20\%

. ✅

C.January-to-February is

20\%

, while February-to-March is

25\%

D.Both increases are

20\%

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: From January to February, the increase is $300$ , so $300/1200=25\%$ . From February to March, the increase is also $300$ , but the original comparison value is now $1,500$ , giving $300/1500=20\%$ . Equal absolute increases can produce different percentages.

Q7. A water tank holds 600 liters initially and later contains 690 liters. A technician computes $90/690\times100\%$ . What is wrong with the calculation, and what is the correct result?

A.Nothing is wrong; the increase is about

13.0\%

B.The denominator should be 600; the increase is

15\%

. ✅

C.The denominator should be 690; the increase is

15\%

D.The change should be

690+600

; the increase is

215\%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The technician used the final amount as the reference. Percent increase compares the change with the starting amount. Since the increase is $690-600=90$ , the correct calculation is $90/600\times100\%=15\%$ .

Q8. A student's score improves from 64 to 76. The student reasons: "The score increased by 12 points, so the percent increase is $12\%$ ." Which response best evaluates the reasoning?

A.Correct, because every point equals one percent.

B.Incorrect, because

12

must be divided by the original score

64

. ✅

C.Incorrect, because

12

must be divided by the new score

76

D.Correct, because the final score is less than 100.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The student correctly identifies the absolute increase as $12$ , but percentage increase requires comparison with the original value. Thus $12/64\times100\%=18.75\%$ . The number of percentage points and percent increase are different ideas.

Q9. A graph shows a company's sales rising from Rs. 2.0 million at Point A to Rs. 2.5 million at Point B. Without relying on the visual height alone, what percent increase does the data represent?

20\%

25\%

✅

50\%

125\%

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The graph's values give an increase of Rs. $0.5$ million. Relative to the original Rs. $2.0$ million, the increase is $0.5/2.0=0.25$ , so the percent increase is $25\%$ . The vertical appearance of a graph can be misleading.

Q10. A company's number of employees changes from 320 to 400. Another department changes from 500 to 600. Which department has the larger percent increase?

A.The first department, because it gained 80 employees. ✅

B.The second department, because it gained 100 employees.

C.Both departments have the same percent increase.

D.There is not enough information to compare them.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The first department increases by $80/320\times100\%=25\%$ . The second increases by $100/500\times100\%=20\%$ . Although the second department gains more employees in absolute terms, the first experiences the greater proportional increase.

Q11. A farmer's crop yield increases from 2,400 kg to 3,000 kg after using a new method. The farmer pays an additional Rs. 12,000 for the method. Which pair correctly describes the yield increase and the additional cost per extra kilogram?

20\%

and Rs. 10 per kg

25\%

and Rs. 20 per kg ✅

25\%

and Rs. 12 per kg

30\%

and Rs. 20 per kg

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The yield increases by $600$ kg, and $600/2400\times100\%=25\%$ . The additional cost per extra kilogram is $12,000/600=$ Rs. 20. Solving both quantities requires distinguishing percent increase from unit cost.

Q12. A graph records website visitors as 8,000 in Week 1, 9,600 in Week 2, and 11,520 in Week 3. Which conclusion is supported by the data?

A.Visitors increased

20\%

each week.

B.Visitors increased

20\%

from Week 1 to Week 2 and

20\%

from Week 2 to Week 3. ✅

C.Visitors increased

16\%

each week.

D.The second increase is larger because the graph rises more steeply.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: From Week 1 to Week 2, the increase is $1,600$ , and $1,600/8,000=20\%$ . From Week 2 to Week 3, the increase is $1,920$ , and $1,920/9,600=20\%$ . The absolute increases differ, but the proportional increases are equal.

Q13. A product's price increases from Rs. 800 to Rs. 920. A second product's price increases from Rs. 1,500 to Rs. 1,710. Which product experienced the greater percent increase, and by how many percentage points?

A.The first by

1

percentage point

B.The second by

1

percentage point

C.The first by

2

percentage points ✅

D.Both are equal

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first product increases by Rs. $120$ , giving $120/800\times100\%=15\%$ . The second increases by Rs. $210$ , giving $210/1500\times100\%=14\%$ . Therefore, the first product's percent increase is larger by $1$ percentage point, not $2$ .

Q14. A researcher reports that a measurement rose from 50 units to 65 units. One method calculates the increase as $65/50\times100\%=130\%$ , while another calculates $(65-50)/50\times100\%=30\%$ . Which method correctly describes the percent increase?

A.The first method, because 65 is the final value.

B.The second method, because it measures the change relative to the original value. ✅

C.Both methods, because they describe the same percentage.

D.Neither method, because percent increase cannot exceed

100\%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The first calculation shows that the final value is $130\%$ of the original, not that it increased by $130\%$ . Percent increase specifically measures the added amount, $65-50=15$ , relative to 50, giving $30\%$ .

🔗 Related Topics (MCQs)

📝 How Use a Problem Solving Strategy MCQs 📝 How to Approach word problems MCQs 📝 How to Use a problem solving strategy for word problems MCQs 📝 How to Solve number problems MCQs 📝 Translate English sentences into algebraic equations MCQs

←Previous Topic:Finding the Whole Given a Part and Percent📝 Find percent increaseFind percent decrease:Next Topic→