Quantitative Aptitude PYQs

Shortcut Trick

Solve using the BODMAS priority: Brackets → Of → Division → Multiplication → Addition → Subtraction.

Expression: 93 − 27 + 38 + 19 − 18 + 44

Sum of positive terms: 93 + 38 + 19 + 44 = 194

Sum of negative terms: 27 + 18 = 45

Final Result: 194 − 45 = 149

∴ The correct answer is 149.

Alternate Method

Given: 93 − 27 + 38 of 1 + 19 ÷ 1 − (18 × 1) + 44

Method Used: Apply the BODMAS rule to solve the arithmetic expression in the correct order.

⇒ 93 − 27 + 38 of 1 + 19 ÷ 1 − (18) + 44 (Solving Brackets)

⇒ 93 − 27 + 38 + 19 ÷ 1 − 18 + 44 (Solving Of: 38 × 1 = 38)

⇒ 93 − 27 + 38 + 19 − 18 + 44 (Solving Division: 19 ÷ 1 = 19)

⇒ (93 + 38 + 19 + 44) − (27 + 18) (Grouping Addition and Subtraction)

⇒ 194 − 45

⇒ 149

∴ The correct answer is 149.

Additional Information

BODMAS Rule

It stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction, defining the order of operations to ensure unique solutions.

Of Operator

The 'of' operator behaves like multiplication but carries a higher priority than division and standard multiplication in the hierarchy.

VBODMAS

An extended version where 'V' stands for Vinculum (bar bracket), which is solved even before standard brackets.

Shortcut Trick

To find the maximum number of boxes, we must calculate the Highest Common Factor (HCF) of the given quantities.

Find the differences between the numbers: 180 − 144 = 36 and 216 − 180 = 36.

Since 36 divides all three numbers (144, 180, and 216) perfectly, the HCF is 36.

∴ The correct answer is 36 boxes.

Alternate Method

Given:

Number of chocolates = 144

Number of toffees = 180

Number of candies = 216

Formula Used:

Maximum number of groups/boxes = HCF(Quantity 1, Quantity 2, Quantity 3)

Calculations:

⇒ Prime factorization of 144 = 2⁴ × 3²

⇒ Prime factorization of 180 = 2² × 3² × 5¹

⇒ Prime factorization of 216 = 2³ × 3³

⇒ HCF = 2^min(4,2,3) × 3^min(2,2,3)

⇒ HCF = 2² × 3² = 4 × 9 = 36

⇒ Total items in each box: Chocolates = 144 ÷ 36 = 4, Toffees = 180 ÷ 36 = 5, Candies = 216 ÷ 36 = 6.

∴ The correct answer is 36 boxes.

Additional Information

Highest Common Factor (HCF)

HCF is the greatest divisor that divides two or more numbers without leaving a remainder. It is also known as GCD (Greatest Common Divisor).

Least Common Multiple (LCM)

LCM is the smallest positive integer that is divisible by each of the given numbers. Relationship: HCF × LCM = Product of two numbers.

Application of HCF

HCF is used to find the maximum possible size of a container, the maximum length of a measuring tape, or the largest number of groups when items are distributed equally.

Shortcut Trick

Factor out 0.5 from the numerator: 0.5 × (0.5 + 0.05) = 0.5 × 0.55 = 0.275.

Now divide by the denominator: 0.275 ÷ 0.1375.

Observe that 1375 × 2 = 2750, so 0.1375 × 2 = 0.2750.

∴ The correct answer is 2.

Alternate Method

Given Expression: ((0.5 × 0.5) + (0.5 × 0.05)) ÷ (0.1375)

Follow the BODMAS rule to simplify the brackets first:

⇒ (0.25 + 0.025) ÷ 0.1375

⇒ 0.275 ÷ 0.1375

To remove the decimals, multiply both numerator and denominator by 10,000:

⇒ 2750 ÷ 1375

⇒ 2

∴ The correct answer is 2.

Additional Information

BODMAS Rule

It stands for Brackets, Of, Division, Multiplication, Addition, and Subtraction, defining the order of operations.

Decimal Division

When dividing decimals, it is often easier to shift the decimal point to the right in both numbers until the divisor is a whole number.

Common Factor Method

The distributive property a × b + a × c = a(b + c) helps in simplifying complex multiplications quickly.

Shortcut Trick

Solve each square root directly by identifying the base numbers:

√20.25 = 4.5 (since 45² = 2025)

√0.36 = 0.6 (since 6² = 36)

√6.25 = 2.5 (since 25² = 625)

√2.25 = 1.5 (since 15² = 225)

Total = 4.5 + 0.6 + 2.5 − 1.5 = 6.1

∴ The correct answer is 6.1.

Alternate Method

Given: √20.25 + √0.36 + √6.25 − √2.25

Method: Convert decimals to fractions to simplify the square root calculation.

⇒ √(2025/100) + √(36/100) + √(625/100) − √(225/100)

⇒ 45/10 + 6/10 + 25/10 − 15/10

⇒ 4.5 + 0.6 + 2.5 − 1.5

⇒ 5.1 + 2.5 − 1.5

⇒ 7.6 − 1.5

⇒ 6.1

∴ The correct answer is 6.1.

Additional Information

Square Root of Numbers Ending in 25

If a number ends in 25, its square root ends in 5. The remaining part of the number is the product of two consecutive integers n × (n + 1). For example, in √2025, 20 = 4 × 5, so the root is 45.

Decimal Point Rule in Square Roots

When taking the square root of a decimal number, the number of decimal places in the result is exactly half of the number of decimal places in the original number.

BODMAS Rule

Always follow the order: Brackets, Orders (roots/powers), Division, Multiplication, Addition, and Subtraction to solve simplification problems correctly.

Shortcut Trick

First, calculate the square roots: √100 = 10, √25 = 5, and √49 = 7.

Solve the expression following BODMAS (Division before Addition): 10 ÷ 5 + 7 = 2 + 7 = 9.

The value of x is 9.

Calculate x² = 9² = 81.

∴ The correct answer is 81.

Alternate Method

Given: x = √100 ÷ √25 + √49

Method: Apply the order of operations (BODMAS/PEMDAS).

⇒ x = 10 ÷ 5 + 7 (since √100 = 10, √25 = 5, and √49 = 7)

⇒ x = 2 + 7 (performing division first)

⇒ x = 9 (performing addition)

⇒ x² = 9²

⇒ x² = 9 × 9

⇒ x² = 81

∴ The correct answer is 81.

Additional Information

BODMAS Rule

This rule dictates the order of operations: Brackets, Orders (powers/roots), Division and Multiplication (left to right), and Addition and Subtraction (left to right).

Perfect Squares

A perfect square is an integer that is the square of an integer. Examples include 25 (5²), 49 (7²), and 100 (10²).

Square Root Property

The square root of a number 'a' is a number 'y' such that y² = a. For calculation, √(a × b) = √a × √b and √(a ÷ b) = √a ÷ √b.

Shortcut Trick

For an odd number of terms, the Average of consecutive numbers is the middle term.

Middle number = 60 ÷ 3 = 20.

The three consecutive even numbers are: 18, 20, 22.

The smallest number in the set is 18.

∴ The correct answer is 18.

Alternate Method

Given:

Sum of three consecutive even numbers = 60.

Formula Used:

Let the three numbers be x, (x + 2), and (x + 4).

Calculations:

⇒ x + (x + 2) + (x + 4) = 60

⇒ 3x + 6 = 60

⇒ 3x = 60 − 6

⇒ 3x = 54

⇒ x = 54 ÷ 3

⇒ x = 18

The smallest number is x = 18.

∴ The correct answer is 18.

Additional Information

Consecutive Even/Odd Numbers

Consecutive even or odd numbers always have a common difference of 2. If the first number is x, the next is x + 2.

Middle Term Shortcut

For any Arithmetic Progression with an odd number of terms (n), the middle term is equal to (Sum of terms) ÷ n.

Average of Consecutive Integers

The Average of a set of consecutive integers is also equal to (First term + Last term) ÷ 2.

Shortcut Trick

Apply the algebraic identity (a + b)(a − b) = a² − b² inside the expression.

Here, a = 21 and b = 11.

⇒ (21 + 11) × (21 − 11) = 21² − 11² = 441 − 121 = 320

The square root and the square exponent cancel each other out, yielding 320.

∴ The correct answer is 320.

Alternate Method

Given:

Expression: (√((21 + 11) × (21 − 11)))²

Formula Used:

(√x)² = x

Calculations:

⇒ First, simplify the terms inside the parentheses:

⇒ 21 + 11 = 32

⇒ 21 − 11 = 10

⇒ Substitute these values back into the expression:

⇒ (√(32 × 10))²

⇒ (√(320))²

⇒ Since the square of a square root of a number is the number itself:

⇒ 320

∴ The correct answer is 320.

Additional Information

Difference of Squares Identity

The formula (a + b)(a − b) = a² − b² is used to quickly find the product of two numbers that are equidistant from a central value.

Square and Square Root Relationship

For any non-negative number x, the operation of squaring and taking the square root are inverse operations, meaning (√x)² = x.

BODMAS Rule

In multi-operator simplification questions, terms inside the innermost brackets are solved first, followed by orders/exponents, division, multiplication, addition, and subtraction.

Shortcut Trick

Sum of existing digits in 58P8 = 5 + 8 + 8 = 21.

The smallest multiple of 9 greater than 21 is 27.

∴ P = 27 − 21 = 6.

∴ The correct answer is 6.

Alternate Method

Given number is 58P8.

According to the Divisibility Rule of 9, a number is divisible by 9 if the sum of its digits is divisible by 9.

⇒ Sum of digits = 5 + 8 + P + 8

⇒ Sum of digits = 21 + P

For the number to be divisible by 9, (21 + P) must be a multiple of 9 {9, 18, 27, 36, ...}.

Since P is a single digit, the possible value for the sum 21 + P is 27.

⇒ 21 + P = 27

⇒ P = 27 − 21

⇒ P = 6

∴ The correct answer is 6.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is divisible by 3 (e.g., 123 → 1+2+3 = 6).

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of digits at odd places and even places is 0 or a multiple of 11.

Divisibility Rule of 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Shortcut Trick

Identify the common surd factor by breaking each term into a perfect square and a remainder.

√48 = 4√3, √27 = 3√3, and √12 = 2√3.

Perform the addition and subtraction: (4 + 3 − 2) × √3 = 5√3.

∴ The correct answer is 5√3.

Alternate Method

Given: √48 + √27 − √12

Method: Simplify each surd by factoring out the largest perfect square from the radicand.

⇒ √48 = √(16 × 3) = 4√3

⇒ √27 = √(9 × 3) = 3√3

⇒ √12 = √(4 × 3) = 2√3

⇒ Expression = 4√3 + 3√3 − 2√3

⇒ Expression = (4 + 3 − 2) × √3

⇒ Expression = 5√3

∴ The correct answer is 5√3.

Additional Information

Simplification of Surds

A surd is in its simplest form when the radicand has no perfect square factors other than 1. Formula: √(a²b) = a√b.

Like and Unlike Surds

Like surds are those that have the same irrational factor.

Only like surds can be added or subtracted directly by combining their coefficients.

Multiplication of Surds

Unlike addition, surds do not need to be like terms for multiplication. The rule follows √a × √b = √(a × b).

Shortcut Trick

Sum of adjacent sides (L + W) = √(Diagonal² + 2 × Area)

L + W = √(20² + 2 × 192) = √(400 + 384) = √784 = 28 cm

Perimeter of Rectangle = 2 × (L + W)

Perimeter = 2 × 28 = 56 cm

∴ The correct answer is 56 cm.

Alternate Method

Given:

Area (L × W) = 192 cm²

Diagonal (d) = 20 cm

Formula Used:

1. d² = L² + W² (by Pythagoras Theorem)

2. (L + W)² = L² + W² + 2LW

3. Perimeter = 2(L + W)

Calculations:

⇒ L² + W² = 20² = 400

⇒ (L + W)² = (L² + W²) + 2(LW)

⇒ (L + W)² = 400 + 2(192)

⇒ (L + W)² = 400 + 384 = 784

⇒ L + W = √784 = 28 cm

⇒ Perimeter = 2 × 28 = 56 cm

∴ The correct answer is 56 cm.

Additional Information

Area of Rectangle

The total space occupied by a rectangle, calculated as Area = length × width.

Diagonal Property

The diagonal of a rectangle divides it into two congruent right-angled triangles, where Diagonal = √(L² + W²).

Algebraic Identity

The identity (a + b)² = a² + b² + 2ab is commonly used to relate Perimeter, Diagonal, and Area.

Perimeter

The total length of the boundary of a rectangle, given by Perimeter = 2(length + width).

Shortcut Trick

If a constant value M is subtracted from every number in a data set, the average of that set also decreases by exactly M.

Initial Average = 34

New Average = 29

Value of M = Initial Average − New Average

M = 34 − 29 = 5

∴ The correct answer is 5.

Alternate Method

Given:

Total numbers (n) = 24

Initial Average = 34

New Average = 29

Formula Used:

Sum of numbers = Average × Count of numbers

Calculations:

⇒ Initial Total Sum = 34 × 24 = 816

⇒ New Total Sum = 29 × 24 = 696

⇒ Total decrease in sum = 816 − 696 = 120

⇒ Since M is subtracted from each of the 24 numbers, the total decrease is 24 × M.

⇒ 24 × M = 120

⇒ M = 120 ÷ 24

⇒ M = 5

∴ The correct answer is 5.

Additional Information

Effect of Addition/Subtraction on Average

If the same value k is added to (or subtracted from) every observation in a set, the new average is the old average plus (or minus) k.

Effect of Multiplication/Division on Average

If every observation is multiplied (or divided) by a non-zero constant k, the average is also multiplied (or divided) by k.

Basic Average Formula

Average = (Sum of all observations) ÷ (Number of observations).

Shortcut Trick

Convert the profit percentage to a fraction: 25% = 1/4.

Profit is 1/4 of the Cost Price (CP).

Profit = 500 ÷ 4 = 125.

∴ The correct answer is Rs.125.

Alternate Method

Given:

Cost Price (CP) = Rs. 500

Profit percentage = 25%

Formula Used:

Profit = (Profit% ÷ 100) × Cost Price

Calculations:

⇒ Profit = (25 ÷ 100) × 500

⇒ Profit = 0.25 × 500

⇒ Profit = 125

∴ The correct answer is Rs.125.

Additional Information

Selling Price (SP) calculation

The price at which an item is sold is SP = CP + Profit. In this case, SP = 500 + 125 = Rs. 625. Cost Price from SP and Profit%

To find Cost Price when SP and Profit% are known: CP = [100 ÷ (100 + Profit%)] × SP.

Loss Calculation

If there is a loss, Loss = CP − SP, and Loss% = (Loss ÷ CP) × 100.

Shortcut Trick

Compare the requested percentage with the given one: 180% is exactly 3 × 60%.

Since the values are directly proportional, multiply the value of 60% by 3.

Required value = 75 × 3 = 225.

∴ The correct answer is 225.

Alternate Method

Given: 60% of a number is 75.

Step-by-step Calculation:

⇒ Let the number be x.

⇒ 60% of x = 75

⇒ (60 ÷ 100) × x = 75

⇒ x = (75 × 100) ÷ 60

⇒ x = 125

⇒ Now, find 180% of the number 125:

⇒ Required Value = (180 ÷ 100) × 125

⇒ Required Value = 1.8 × 125

⇒ Required Value = 225

∴ The correct answer is 225.

Additional Information

Unitary Method in Percentage

If a% of a number is V₁, then b% of the same number is (V₁ ÷ a) × b.

Percentage to Fraction

To convert percentage to fraction, divide by 100. For example, 180% = 180 ÷ 100 = 9/5.

Base Value Calculation

The original number (100%) is called the base value and can be found using: Value ÷ Percentage Rate.

Shortcut Trick

Total Maximum Marks = 5 × 200 = 1000

Total Marks Obtained = 60% of 1000 = 600

Marks in Subject 1 = 25% of 600 = 1/4 × 600 = 150

∴ The correct answer is 150.

Alternate Method

Given:

Total subjects = 5

Maximum marks per subject = 200

Total percentage scored = 60%

Subject 1 score = 25% of the total marks obtained

Formula Used:

Total Marks Obtained = (Percentage ÷ 100) × Total Maximum Marks

Subject Score = (Subject % ÷ 100) × Total Marks Obtained

Calculations:

⇒ Total maximum marks for 5 subjects = 5 × 200 = 1000

⇒ Total marks obtained by the student = (60 ÷ 100) × 1000 = 600

⇒ Score in Subject 1 = 25% of 600

⇒ Score in Subject 1 = (25 ÷ 100) × 600

⇒ Score in Subject 1 = 0.25 × 600 = 150

∴ The correct answer is 150.

Additional Information

Percentage of a Quantity

To find x% of a value Y, the formula is (x ÷ 100) × Y. This is essential for calculating marks, discounts, and taxes.

Average Marks Calculation

Average marks per subject = Total Marks Obtained ÷ Number of Subjects. Here, Average = 600 ÷ 5 = 120.

Fraction to Percentage Conversion

To convert a fraction to a percentage, multiply by 100. Common fractions include 1/4 = 25%, 1/2 = 50%, and 3/4 = 75%.

Shortcut Trick

30% of Cost Price = 25% of Selling Price

⇒ CP : SP = 25 : 30 = 5 : 6

⇒ Profit = 6 − 5 = 1 unit

⇒ Profit Percentage = (1 / 5) × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given: 30% of Cost Price (CP) is equal to 25% of Selling Price (SP).

Formula Used: Profit Percentage = [(Selling Price − Cost Price) ÷ Cost Price] × 100

⇒ (30/100) × CP = (25/100) × SP

⇒ 30 × CP = 25 × SP

⇒ CP / SP = 25 / 30 = 5 / 6

⇒ Let Cost Price = 5 units and Selling Price = 6 units

⇒ Profit = Selling Price − Cost Price = 6 − 5 = 1 unit

⇒ Profit Percentage = (1 / 5) × 100

⇒ Profit Percentage = 20%

∴ The correct answer is 20%.

Additional Information

Marked Price and Discount

The Marked Price is the price tag on an item. Discount is always calculated as a percentage of the Marked Price.

Loss Percentage

If Cost Price is greater than Selling Price, it is a Loss. Loss % = [(CP − SP) / CP] × 100.

Successive Discounts

Equivalent discount for two successive discounts a% and b% = [a + b − (ab / 100)]%.

Shortcut Trick

Work done in 10 days = 50%

Work done in 1 day = 50% ÷ 10 = 5%

Work done in 7 days = 5% × 7 = 35%

∴ The correct answer is 35%.

Alternate Method

Given:

Time taken by A to complete 50% work = 10 days

Time taken by A to complete 100% work = 10 × (100 ÷ 50) = 20 days

⇒ Total Work (LCM of 20) = 20 units

⇒ Efficiency of A = Total Work ÷ Time = 20 ÷ 20 = 1 unit per day

⇒ Work completed by A in 7 days = Efficiency × Time = 1 × 7 = 7 units

⇒ Part of work completed (in %) = (Work Done ÷ Total Work) × 100

⇒ Percentage = (7 ÷ 20) × 100

⇒ Percentage = 35%

∴ The correct answer is 35%.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If time taken is T, then Efficiency E = 1 ÷ T.

The M-D-H Formula

For comparing two work scenarios: (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where M is men, D is days, H is hours, and W is work.

Work Rate

Total Work = Efficiency × Time. For a single person, the portion of work done in 't' days is (t ÷ Total Days) × 100%.

Shortcut Trick

When (P+Q) and R work together, the combined time is calculated by the Product/Sum formula.

Total Time = (Time_(P+Q) × Time_R) ÷ (Time_(P+Q) + Time_R)

Time = (20 × 30) ÷ (20 + 30)

Time = 600 ÷ 50 = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

Time taken by (P+Q) = 20 days

Time taken by R = 30 days

Formula Used:

Efficiency = Total Work ÷ Time taken

Total Work = LCM of 20 and 30 = 60 units

Calculations:

⇒ Total efficiency of (P + Q + R) = Efficiency of (P + Q) + Efficiency of R

⇒ Total efficiency = 3 + 2 = 5 units/day

⇒ Total time taken = Total Work ÷ Total efficiency

⇒ Total time = 60 ÷ 5

⇒ Total time = 12 days

∴ The correct answer is 12 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If Efficiency ratio is a:b, then Time ratio is b:a.

Combined Work Formula

If two entities A and B take x and y days respectively, then working together they take (x × y) ÷ (x + y) days.

Work and Wages

Wages are generally distributed in the ratio of work done or the ratio of efficiencies when they work for the same duration.

Shortcut Trick

To convert speed from m/s to km/hr, directly multiply the given value by 18/5.

Given Speed = 100 m/s

Speed (km/hr) = 100 × (18 ÷ 5) = 20 × 18 = 360 km/hr.

∴ The correct answer is 360 km/hr.

Alternate Method

Given: Speed of the train = 100 m/s

Formula Used: 1 m/s = (1 ÷ 1000) km / (1 ÷ 3600) hr = 3.6 km/hr

⇒ Speed = 100 m/s

⇒ Speed in km/hr = 100 × (3600 ÷ 1000)

⇒ Speed in km/hr = 100 × 3.6

⇒ Speed = 360 km/hr

∴ The correct answer is 360 km/hr.

Additional Information

km/hr to m/s Conversion

To convert speed from km/hr to m/s, multiply by 5/18. For example, 36 km/hr = 36 × 5/18 = 10 m/s.

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. If a body travels equal distances at speeds x and y, the average speed is 2xy ÷ (x + y).

Relative Speed

For two objects moving in the opposite direction, relative speed = S₁ + S₂. For the same direction, relative speed = S₁ − S₂.

Shortcut Trick

Ratio of Speed of Train to Man = 4 : 1

Since they move in opposite direction, Relative Ratio = 4 + 1 = 5 units

Relative Speed = Distance ÷ Time = 800 ÷ 8 = 100 m/s

5 units = 100 m/s ⇒ 1 unit = 20 m/s

Speed of Train (4 units) = 4 × 20 = 80 m/s

In km/hr: 80 × (18/5) = 288 km/hr

∴ The correct answer is 288 km/hr.

Alternate Method

Given:

Length of Train (L) = 800 m

Time taken (t) = 8 seconds

Let the Speed of Man be v m/s.

⇒ Speed of Train = 4v m/s

Formula:

Relative Speed (Opposite) = Speed of Train + Speed of Man

Relative Speed = Distance ÷ Time

Calculations:

⇒ 4v + v = 800 ÷ 8

⇒ 5v = 100

⇒ v = 20 m/s

⇒ Speed of Train = 4 × 20 = 80 m/s

⇒ To convert m/s to km/hr, multiply by 18/5:

⇒ Speed in km/hr = 80 × (18/5)

⇒ Speed in km/hr = 16 × 18

⇒ Speed in km/hr = 288 km/hr

∴ The correct answer is 288 km/hr.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂). If moving in the same direction, it is the difference |S₁ − S₂|.

Speed Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Train Crossing a Moving Object

When a train crosses a man, pole, or tree, the total distance covered is always equal to the length of the train itself.

Shortcut Trick

Assume the Marked Price (MP) of the article is 100 units.

Cost Price (CP) for the person = 100 − 25% of 100 = 75 units.

Selling Price (SP) for the person = 100 + 30% of 100 = 130 units.

Profit percentage = [(130 − 75) ÷ 75] × 100 = (55 ÷ 75) × 100 = 73.33%.

∴ The correct answer is 73.33 percent.

Alternate Method

Given: Marked Price = X, Discount = 25% of MP, Selling Price = X + 30% of X.

Formula Used: Profit % = [(SP − CP) ÷ CP] × 100

⇒ Cost Price (CP) = X − 0.25X = 0.75X

⇒ Selling Price (SP) = X + 0.30X = 1.30X

⇒ Profit = SP − CP = 1.30X − 0.75X = 0.55X

⇒ Profit % = (0.55X ÷ 0.75X) × 100

⇒ Profit % = (55 ÷ 75) × 100 = 11/15 × 100 = 73.333...

⇒ Profit % ≈ 73.33%

∴ The correct answer is 73.33 percent.

Additional Information

Marked Price (MP) and Discount

Discount is always calculated on the Marked Price. SP = MP × (100 − Discount%) ÷ 100.

Profit/Loss Basis

Unless specified, Profit or Loss percentage is always calculated on the Cost Price (CP).

Successive Percentage Change

When a value changes by a% and then b%, the net change is given by the formula: [a + b + (ab ÷ 100)]%.