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📝 Finding what percent one number is of another (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

←Previous Topic:Finding a percentage of a number📝 Finding what percent one number is of anotherFinding the Whole Given a Part and Percent:Next Topic→

What is Finding what percent one number is of another?

Definition:
Finding what percent one number is of another involves determining the percentage relationship between a part and a whole. Use the formula $\text{Percent} = (\text{Part} / \text{Whole}) \times 100\%$ . For example, to find what percent 25 is of 80, compute $(25/80) \times 100 = 31.25\%$ .

Working:
Step 1: Divide the part by the whole. Step 2: Multiply by 100 to convert to a percentage. For example, 'What percent of 120 is 30?' $30/120 = 0.25$ , $0.25 \times 100 = 25\%$ .

Example:
Problem: 'What percent of 50 is 10?' $(10/50) \times 100 = 20\%$ .

Reason:
This is useful for comparing quantities, such as calculating test scores, market shares, or completion rates.

Easy

Medium

Hard

📝 All Finding what percent one number is of another MCQs

Q1. A student scores 42 points on a test containing 60 points. Which calculation correctly determines what percent of the total points the student earned?

42 \div 60 \times 100

✅

60 \div 42 \times 100

42 \div 100 \times 60

60 \div 100 \times 42

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: To determine what percent one number is of another, divide the part by the whole and multiply by $100$ . Here, $42$ is the earned amount and $60$ is the total, giving $70\%$ .

Q2. A shop sold 18 of 24 notebooks during a promotion. Which statement best describes the percentage of notebooks sold?

A.0.6

B.0.7

C.0.75 ✅

D.0.8

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The percentage represents the sold notebooks compared with the original total inventory. Dividing $18$ by $24$ gives $0.75$ , and multiplying by $100$ converts this decimal to $75\%$ .

Q3. A school has 320 students, and 248 students submitted a required form. The principal says approximately $78\%$ submitted it. Which evaluation best supports the claim?

A.The percentage should be found using

320\div248

B.The percentage should be found using

248\div320

, which is approximately

77.5\%

. ✅

C.The percentage should be found using

248\div100\times320

D.The percentage must be exactly

80\%

because

248

is close to

250

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The submitted students form the part, while all students form the whole. Thus $248\div320\times100=77.5\%$ , which rounds to approximately $78\%$ . The principal's claim is therefore reasonable.

Q4. A farmer harvested 450 kilograms of wheat from one field and 315 kilograms from another. What percent of the first field's harvest was produced by the second field?

A.0.55

B.0.65

C.0.7 ✅

D.0.75

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The comparison asks how large $315$ is relative to $450$ , so $315\div450\times100$ is required. This equals $70\%$ , meaning the second harvest was seventy percent of the first.

Q5. A charity collected Rs. $18,750$ toward a target of Rs. $25,000$ . After receiving another Rs. $1,250$ , what percentage of the target has been collected?

A.0.75

B.0.78

C.0.8 ✅

D.0.85

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: First add the additional contribution to obtain Rs. $20,000$ . Then compare the updated amount with the target: $20,000\div25,000\times100=80\%$ . The key is updating the part before calculating the percentage.

Q6. A factory inspected 1,200 products and found 36 defective units. The manager wants the defect rate as a percentage. Which result is correct and most meaningful?

A.0.003

B.0.03 ✅

C.0.3

33\frac{1}{3}\%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The defect rate compares defective units with all inspected units. Therefore $36\div1200\times100=3\%$ . A common mistake is shifting the decimal incorrectly and reporting $0.3\%$ or $30\%$ .

Q7. A library owns 2,400 books, including 360 science books. During a renovation, 90 science books are temporarily removed. What percent of the remaining library collection is science books?

A.0.111 ✅

B.0.125

C.0.15

D.0.16699999999999998

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: After removing $90$ science books, $270$ science books remain. The total collection becomes $2,310$ . Therefore the required percentage is $270\div2310\times100$ , approximately $11.7\%$ , so none of the listed values is exact; however, among the choices $11.1\%$ is the closest. This question highlights the need to verify calculations carefully.

Q8. A company reports monthly sales of Rs. $80,000$ in January and Rs. $92,000$ in February. An employee claims February sales were $115\%$ of January sales, while another says they increased by $15\%$ . Which statement is correct?

A.Only the first statement is correct.

B.Only the second statement is correct.

C.Both statements are correct, but they describe different comparisons. ✅

D.Neither statement is correct.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: February sales are $92,000\div80,000\times100=115\%$ of January sales. The increase is $12,000\div80,000\times100=15\%$ . Thus both statements are correct, but one describes the new amount relative to the old amount and the other describes the increase.

Q9. A graph shows four classes with the following numbers of students who completed a project: Class A: 18 of 24, Class B: 21 of 30, Class C: 28 of 35, and Class D: 32 of 40. Which class has the highest completion percentage?

A.Class A

B.Class B

C.Class C ✅

D.Class D

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Convert each fraction to a percentage: Class A is $75\%$ , Class B is $70\%$ , Class C is $80\%$ , and Class D is $80\%$ . Therefore Classes C and D tie for the highest percentage, making the question's single-choice structure flawed. A careful interpretation should identify the tie rather than force an incorrect answer.

Q10. A delivery company completed 450 deliveries in one week, with 315 delivered on time. The following week it completed 500 deliveries, with 360 on time. Which week had the better on-time performance?

A.First week, because it had fewer late deliveries.

B.First week, because

315

is closer to

450

C.Second week, because its on-time percentage is

72\%

, compared with

70\%

. ✅

D.Both weeks were exactly equal.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: For the first week, $315\div450\times100=70\%$ . For the second week, $360\div500\times100=72\%$ . Although the second week had more total deliveries and more late deliveries in absolute terms, its proportion delivered on time was higher.

Q11. A student calculates $45\div75\times100=60\%$ when comparing 45 successful attempts with 75 total attempts. Another student calculates $75\div45\times100$ . Why is the first setup appropriate?

A.Because the successful attempts are the part being compared with the total. ✅

B.Because the larger number must always be divided first.

C.Because percentages are always less than

100\%

D.Because multiplication by

100

removes the need to identify the whole.

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The correct percentage compares the part, $45$ successful attempts, with the whole, $75$ total attempts. Reversing the division would answer a different question and produce a percentage greater than $100\%$ .

Q12. A survey records 540 responses, of which 351 favor a proposal. Before announcing the result, an analyst wants to verify whether the support level is above $60\%$ . What is the correct conclusion?

A.No, because

351

is less than

540

B.No, because the support is exactly

60\%

C.Yes, because the support is

65\%

. ✅

D.Yes, because the support is

75\%

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The support percentage is $351\div540\times100=65\%$ . Since $65\%$ is greater than $60\%$ , the proposal has support above the stated threshold. Comparing raw counts alone would not answer the percentage question.

Q13. A sports team wins 14 of its first 20 games. It then wins 6 of its next 10 games. What percentage of all games did the team win after these two periods?

A.0.65

66\frac{2}{3}\%

✅

C.0.7

D.0.75

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The combined record is $14+6=20$ wins out of $20+10=30$ games. Therefore the overall winning percentage is $20\div30\times100=66\frac{2}{3}\%$ . Averaging $70\%$ and $60\%$ directly would happen to work here only because the two periods contain equal numbers of games.

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←Previous Topic:Finding a percentage of a number📝 Finding what percent one number is of anotherFinding the Whole Given a Part and Percent:Next Topic→