UGC NET Questions (Paper – 1)

In commercial mathematics, if the selling price (SP) of an item is greater than its cost price (CP), the trader gains money on the transaction. This gain is called profit and is calculated as SP − CP. Profit indicates that the trader has sold the item for more than it cost to acquire. Therefore, the situation described in the question corresponds exactly to making a profit.

Option A:
Loss occurs when the cost price exceeds the selling price, meaning the trader receives less money than was spent on purchasing the item. This is the opposite situation to what is described in the question, where selling price is higher than cost price. Hence, loss cannot be the correct answer here.

Option B:
Profit is correct because it is the name given to the positive difference SP − CP when SP > CP. For example, if an article costs ₹500 and is sold for ₹600, the trader makes a profit of ₹100. Recognising this condition quickly is useful in many UGC NET aptitude problems involving multiple stages of buying and selling.

Option C:
A discount is a reduction given on the marked price of an item, usually to attract customers, and is calculated before determining the final selling price. While discounts can affect profit, the term itself does not directly describe the situation SP > CP. Therefore, discount does not match the definition in the stem.

Option D:
Commission is a fee or percentage of sales paid to an agent or salesperson for services rendered. It is not the difference between selling price and cost price. Since the question focuses on the trader's gain from SP exceeding CP, commission is not the appropriate term.

This option is correct because the percentage increase is calculated as (increase ÷ original value) × 100. The increase is 120 − 100 = 20. So, (20 ÷ 100) × 100 = 20%. Therefore, the price has increased by 20%.

Option A:
The increase of ₹20 over an original price of ₹100 represents 20% of the original. This is obtained directly from the formula and matches intuitive understanding. Hence, 20% is the correct percentage increase.

Option B:
A 10% increase on ₹100 would be ₹10, giving a final price of ₹110. The actual new price is ₹120, so 10% underestimates the change. Therefore, this option is wrong.

Option C:
A 15% increase would add ₹15, resulting in a price of ₹115. This still does not reach the actual new price of ₹120. Thus, 15% is not the correct percentage increase.

Option D:
A 25% increase on ₹100 would be ₹25, leading to a price of ₹125. This overshoots the given new price, so 25% is too high. Hence, this option is incorrect.

C and E are wrong because they contradict basic properties and uses of ratios. Ratios can indeed be simplified by dividing both terms by the same non-zero number, in the same way that fractions are simplified, so C is false. E is also false because ratio and proportion are central to many aptitude problems, especially those involving sharing, mixtures and scaling. A, B and D all correctly describe comparison, equality in proportion and sharing applications, so the wrong statements are exactly C and E.

Option A:
Option A is incorrect because it identifies only C as wrong and overlooks E, which dismisses the importance of ratios in aptitude, a claim that clearly conflicts with the UGC NET syllabus. Leaving out E means not all wrong statements are captured.

Option B:
Option B is also incorrect since it treats only E as wrong and ignores C, which incorrectly states that ratios cannot be simplified. A proper understanding of ratio includes the idea of simplification.

Option C:
Option C is correct because it brings together both C and E, the two statements that misrepresent ratio properties and their examination relevance. It implicitly acknowledges that A, B and D provide accurate descriptions used in aptitude questions.

Option D:
Option D is wrong because it adds B, which is true about cross products in a proportion, to the set of supposed wrong statements. Including B makes the option inconsistent with the mathematical definition of proportion.

The arithmetic mean of five numbers is 18, so their total sum is 18 × 5 = 90. One of the numbers is given as 24. To find the sum of the remaining four numbers, we subtract this known value from the total: 90 − 24 = 66. Thus, the combined total of the four remaining numbers is 66.

Option A:
Option A directly applies the relationship Total = Average × Number of items and then subtracts the known element to obtain the sum of the others. This method is standard in average problems and yields 66 consistently.

Option B:
Option B, 72, would correspond to a larger total of 96 if 24 were added back, which would produce an average of 19.2 instead of 18. This contradicts the given mean.

Option C:
Option C, 80, similarly gives a total of 104 when 24 is added back, leading to an average of 20.8, which is inconsistent with the initial information.

Option D:
Option D, 84, implies a total of 108 for five numbers, resulting in an average of 21.6, again conflicting with the given average of 18.

If the average of two numbers is 20, their total sum must be 20 × 2 = 40. One of the numbers is given as 16. To find the other number, we subtract the known number from the total: 40 − 16 = 24. Therefore, the second number must be 24 so that the pair has an average of 20.

Option A:
Option A, 18, would result in a total of 34 when added to 16, which would give an average of 17, not 20. Thus, it underestimates the required second number.

Option B:
Option B, 20, would give a total of 36 and an average of 18, which again does not meet the given condition of average 20.

Option C:
Option C, 22, makes the total 38, leading to an average of 19, which is close but still not equal to 20.

Option D:
Option D maintains the correct relation: 16 + 24 = 40, and 40 ÷ 2 = 20, so the pair (16, 24) satisfies the stated average exactly.

This option is correct because 50% means 50 out of 100. Writing this as a fraction gives 50/100. Dividing numerator and denominator by their greatest common divisor 50 gives 1/2. Therefore, 50% equals the fraction 1/2.

Option A:
The fraction 1/3 corresponds to approximately 33.33%, not 50%. It does not represent half of a whole. Hence, this option is not correct.

Option B:
The fraction 1/4 is equal to 25%, which is half of 50%. Therefore, 1/4 is too small to match 50%. So, this option is incorrect.

Option C:
The fraction 1/2 represents exactly half of a unit, which matches the idea of 50%. Converting back to a percentage gives 0.5 × 100 = 50%. Thus, this option correctly expresses 50% as a fraction.

Option D:
The fraction 2/3 corresponds to about 66.67%, which is greater than 50%. Therefore, it does not represent 50% and cannot be the correct answer.

Statements A, C and D all describe standard facts from elementary number theory. Every prime greater than 2 is odd because 2 is the only even prime. Composite numbers must have at least one additional divisor besides 1 and themselves, giving at least three distinct positive divisors. There are infinitely many primes, a result known since Euclid’s proof. Statements B and E are false because 1 is neither prime nor composite and many even numbers greater than 2, such as 4, 6 and 8, are not prime, so A, C and D only are correct.

Option A:
Option A is correct because it picks exactly those statements that are true and excludes the common misconceptions in B and E. It recognises that 1 is excluded from the definition of primes and that even numbers beyond 2 are usually composite. By including C, it also captures a key structural property of composite numbers.

Option B:
Option B is incorrect as it omits D, thereby ignoring the important theorem that there are infinitely many primes. Even though it includes two true statements, it fails to include all the correct ones.

Option C:
Option C is wrong because it brings in E, which incorrectly claims that every even number greater than 2 is prime. Introducing a clearly false statement alongside A and D makes the overall combination incorrect.

Option D:
Option D is incomplete since it includes only C and D and leaves out A. While C and D are true, this option fails to capture the basic fact that primes greater than 2 are odd, so it does not list the full set of correct statements.

To find the LCM, we factor each number into primes. The factorization of 6 is 2 × 3, of 8 is 2³ and of 9 is 3². The LCM must contain the highest powers of each prime present, so it is 2³ × 3² = 8 × 9 = 72. This is the smallest number divisible by 6, 8 and 9 without remainder.

Option A:
Option A, 36, is divisible by 6 and 9 but not by 8, because 36 ÷ 8 is not an integer. Thus, it fails the requirement of being a common multiple of all three numbers.

Option B:
Option B correctly uses the highest powers of primes appearing in the factorization of each number. By combining 2³ and 3², we ensure divisibility by 6, 8 and 9, and 72 is the least such number.

Option C:
Option C, 48, is divisible by 6 and 8 but not by 9, as 48 ÷ 9 is not an integer. Therefore, it cannot be the LCM.

Option D:
Option D, 54, is divisible by 6 and 9 but not by 8, since 54 ÷ 8 is not a whole number. It is a common multiple of only two of the three numbers.

This option is correct because simplifying a ratio involves dividing both terms by their greatest common divisor. The greatest common divisor of 8 and 12 is 4. Dividing both by 4 gives 8:12 = 2:3. Therefore, the simplest form of the ratio is 2:3.

Option A:
The ratio 3:2 reverses the order of the terms and does not preserve the original relationship. It corresponds to 12:8 after scaling, which is not equal to 8:12. Thus, this option is incorrect.

Option B:
The ratio 4:6 is equivalent to 8:12 but not in simplest form. Both terms still have a common factor of 2. Since we can reduce further to 2:3, 4:6 is not fully simplified.

Option C:
The ratio 2:3 is obtained by dividing both 8 and 12 by 4. It has no further common factor greater than 1, so it is in simplest form. This matches the standard requirement for simplified ratios.

Option D:
The ratio 1:3 would correspond to 4:12 when scaled up, which is different from 8:12. Therefore, 1:3 does not represent the same relationship and is not correct.

The ratio 3 : 2 indicates that out of every 5 equal parts, 3 parts represent boys and 2 parts represent girls. The total number of parts is therefore 3 + 2 = 5. If 5 parts correspond to 90 students, then 1 part equals 90 ÷ 5 = 18 students. The number of boys is 3 parts, which is 3 × 18 = 54.

Option A:
Option A, 36, corresponds to 2 parts of 18 instead of 3, which would actually represent the number of girls if the same logic is applied correctly to the ratio. Hence, it mismatches the role of boys in the ratio.

Option B:
Option B, 45, is obtained if someone wrongly assumes 90 × (1/2) but that would correspond to a hypothetical 1 : 1 ratio. It does not respect the actual 3 : 2 proportion given in the question.

Option C:
Option C follows the correct ratio method: convert the total into parts, find the value of one part and then multiply by the number of parts corresponding to boys. This systematic approach yields 54, aligning with the structure of the ratio.

Option D:
Option D, 60, would imply that boys form two thirds of the class, which does not fit a 3 : 2 ratio where boys are 3/5 of the total. It clearly exceeds the value compatible with the defined proportion.

Percentage is calculated by dividing the obtained marks by the maximum marks and then multiplying by 100. Here the student’s score is 40 out of 80, so the fraction is 40 ÷ 80 = 1/2. Converting this fraction to a percentage gives (1/2) × 100 = 50%. Therefore, the student has obtained half of the total marks, which is 50%.

Option A:
Option A, 40%, would be correct if the student had scored 40 out of 100, but the total here is only 80. It fails to account for the correct denominator in the percentage calculation.

Option B:
Option B, 45%, has no direct basis in the ratio 40 : 80 and likely arises from a guess or miscalculation. It does not correspond to any simple fraction equivalent of 1/2.

Option C:
Option C, 55%, would indicate that the student scored slightly more than half, but numerically 40 is exactly half of 80, not more. Thus, it is not consistent with the actual score.

Option D:
Option D matches the exact fraction of marks obtained relative to the total. By correctly applying the formula (obtained/total) × 100, we arrive at 50%, which accurately represents the student’s performance.

The expression 300 + 40 + 5 represents the sum of hundreds, tens and units. Adding them stepwise, 300 + 40 = 340 and then 340 + 5 = 345. This matches the standard place value representation of the three-digit number 345. Hence, the combined value is 345.

Option A:
Option A correctly aligns each term with its place value: 300 in the hundreds place, 40 in the tens place and 5 in the ones place. Adding them produces 345, which is the number whose digits reflect these contributions.

Option B:
Option B, 354, rearranges the tens and ones positions compared to the calculation and cannot be produced by this particular sum of components.

Option C:
Option C, 435, places the 4 in the hundreds place instead of the tens place, which would require 400 rather than 40 as one of the terms.

Option D:
Option D, 453, similarly misplaces the digits and implies 400 + 50 + 3 rather than 300 + 40 + 5.

This option is correct because converting a fraction to a percentage involves multiplying by 100. For 1/4, we compute (1/4) × 100 = 25. Writing this as a percentage gives 25%. Therefore, 1/4 is equivalent to 25%.

Option A:
25% means 25 parts out of 100, which simplifies to the fraction 25/100. Reducing 25/100 by dividing numerator and denominator by 25 gives 1/4. This confirms that 1/4 and 25% represent the same value.

Option B:
20% corresponds to 20/100, which simplifies to 1/5. Since 1/5 is different from 1/4, this percentage does not match the given fraction. Hence, this option is incorrect.

Option C:
40% corresponds to 40/100, which reduces to 2/5. This fraction again differs from 1/4. Therefore, 40% cannot be the correct conversion.

Option D:
50% represents 50/100, which simplifies to 1/2. This is larger than 1/4 and does not equal it. Thus, this option is also not correct.

To find 15% of 200, we interpret 15% as 15 out of 100. The calculation is (15 ÷ 100) × 200. Simplifying, 15 × 2 = 30, so the result is 30. Thus, 15% of 200 equals 30.

Option A:
Option A, 25, corresponds to 12.5% of 200 and arises if someone confuses 1/8 with 15%. It does not follow from the correct percentage calculation.

Option B:
Option B matches the formula for a percentage of a quantity and uses the simple fraction representation of 15%. The arithmetic shows that 30 is the exact proportion of 200 described by 15%.

Option C:
Option C, 35, is greater than 30 and would correspond to 17.5% of 200, not 15%. It therefore overestimates the desired portion.

Option D:
Option D, 40, equals 20% of 200 and is again inconsistent with the requested 15% rate.

The ratio 3 : 5 means that for every 3 parts of the smaller number there are 5 parts of the larger number. If 3 parts correspond to 24, then 1 part is 24 ÷ 3 = 8. The larger number has 5 such parts, so it is 5 × 8 = 40. Thus, a pair of numbers 24 and 40 has the ratio 3 : 5.

Option A:
Option A, 30, would make the ratio 24 : 30, which simplifies to 4 : 5, not 3 : 5. So it does not preserve the given ratio between the numbers.

Option B:
Option B, 36, gives a ratio of 24 : 36, which reduces to 2 : 3. This is again different from the required 3 : 5 and does not meet the condition.

Option C:
Option C, 40, is obtained by scaling the ratio correctly: each part is 8 and the larger number gets 5 parts. This respects the original ratio 3 : 5 and maintains the exact proportional relationship.

Option D:
Option D, 45, would produce 24 : 45, which does not simplify to 3 : 5 and therefore cannot be accepted as consistent with the given ratio.