Quantitative Aptitude PYQs

Shortcut Trick

Solve the bracket first: (39 + 16) = 55.

Perform multiplication: 55 × 2 = 110.

Sum the positive terms: 65 + 83 + 110 = 258.

Sum the negative terms: 44 + 88 = 132.

Calculate the difference: 258 − 132 = 126.

∴ The correct answer is 126.

Alternate Method

Given:

65 + 83 − 44 + (39 + 16) × 2 − 88 = ?

Formula used:

Follow the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction).

Calculations:

⇒ ? = 65 + 83 − 44 + (55) × 2 − 88

⇒ ? = 65 + 83 − 44 + 110 − 88

⇒ ? = 148 − 44 + 110 − 88

⇒ ? = 104 + 110 − 88

⇒ ? = 214 − 88

⇒ ? = 126

∴ The correct answer is 126.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets ( ), Orders/Of, Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

Grouping Terms

In long addition and subtraction strings, grouping positive and negative values separately can minimize errors.

Types of Brackets

Always solve from inner to outer: Parentheses ( ), Braces { }, and Square Brackets [ ].

Shortcut Trick

Solve using the BODMAS sequence: 53 + 45 − 18 + (66 ÷ 6) − (24 × 1) + 37.

Perform Division and Of operations first: 11 and 24.

Combine all positive values: 53 + 45 + 11 + 37 = 146.

Subtract the total negative values: 146 − (18 + 24) = 146 − 42 = 104.

∴ The correct answer is 104.

Alternate Method

Given expression: 53 + 45 − 18 + 66 ÷ 6 − (24 of 1) + 37

According to the BODMAS rule, we solve in order: Brackets, Of, Division, Multiplication, Addition, and Subtraction.

⇒ 53 + 45 − 18 + 66 ÷ 6 − 24 + 37 (Solving Of/Bracket)

⇒ 53 + 45 − 18 + 11 − 24 + 37 (Solving Division)

⇒ 98 − 18 + 11 − 24 + 37 (Solving Addition from left)

⇒ 80 + 11 − 24 + 37

⇒ 91 − 24 + 37

⇒ 67 + 37

⇒ 104

∴ The correct answer is 104.

Additional Information

BODMAS Rule

It defines the order of operations to solve mathematical expressions: B (Brackets), O (Of), D (Division), M (Multiplication), A (Addition), S (Subtraction).

Of Operator

The word Of represents multiplication but must be performed before division and after brackets in any simplification problem.

V-BODMAS

The V stands for Vinculum (a bar bracket like —), which is solved even before standard round brackets.

Shortcut Trick

Separate the whole number part and the decimal part for quick calculation.

Sum of whole numbers = 420 + 42 + 4 + 0 = 466

Sum of decimal numbers = 0.005 + 0.2005 + 0.42005 = 0.62555

Total summation = 466 + 0.62555 = 466.62555

∴ The correct answer is 466.62555.

Alternate Method

Given: 420, 42.005, 4.2005, 0.42005

To add decimal numbers, convert them into like decimals by adding placeholder zeros so that each number has five decimal places.

⇒ 420.00000

⇒ 042.00500

⇒ 004.20050

⇒ 000.42005

Performing column addition by aligning the decimal points:

⇒ 420.00000 + 42.00500 + 4.20050 + 0.42005 = 466.62555

∴ The correct answer is 466.62555.

Additional Information

Like Decimals

Decimals having the same number of digits after the decimal point are called like decimals. This is essential for accurate column addition.

Place Value in Decimals

Each position after the decimal point represents a power of 10 in the denominator: tenths (10⁻¹), hundredths (10⁻²), thousandths (10⁻³), etc.

BODMAS Rule

In more complex simplifications, always follow the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) priority for calculations.

Shortcut Trick

The given expression follows the pattern of the algebraic identity a³ − 3a²b + 3ab² − b³ = (a − b)³.

Identify a = 2.5 and b = 0.5 from the terms.

Direct calculation: (2.5 − 0.5)³ = (2)³.

Final result: 8.

∴ The correct answer is 8.0.

Alternate Method

Given: (2.5)² × 2.5 − 3 × 0.5 × (2.5)² + 3 × 2.5 × (0.5)² − (0.5)³

Formula used: (a − b)³ = a³ − 3a²b + 3ab² − b³

⇒ Let the variable a = 2.5 and b = 0.5.

⇒ Substituting these values into the given expression:

⇒ a³ − 3a²b + 3ab² − b³

⇒ This is equivalent to (a − b)³.

⇒ (2.5 − 0.5)³

⇒ (2.0)³

⇒ 2 × 2 × 2 = 8

∴ The correct answer is 8.0.

Additional Information

Standard Algebraic Cubic Identities

(a + b)³ = a³ + 3a²b + 3ab² + b³ and (a − b)³ = a³ − 3a²b + 3ab² − b³.

Difference and Sum of Cubes

a³ − b³ = (a − b)(a² + ab + b²) and a³ + b³ = (a + b)(a² − ab + b²).

Special Case

If a + b + c = 0, then a³ + b³ + c³ = 3abc.

Shortcut Trick

The sum of the first n natural numbers is given by the formula: [n × (n + 1)] ÷ 2.

Here, the series ends at 30, so n = 30.

Applying the values: (30 × 31) ÷ 2 ⇒ 15 × 31.

Result = 465.

∴ The correct answer is 465.

Alternate Method

Given:

The series is an Arithmetic Progression (AP): 1, 2, 3, ..., 30.

First term (a) = 1

Last term (l) = 30

Number of terms (n) = 30

Formula Used:

Sum of AP = (n ÷ 2) × (a + l)

Calculations:

⇒ Sum = (30 ÷ 2) × (1 + 30)

⇒ Sum = 15 × 31

⇒ Sum = 465

∴ The correct answer is 465.

Additional Information

Sum of Squares of First n Natural Numbers

The formula for the sum 1² + 2² + ... + n² is [n(n + 1)(2n + 1)] ÷ 6.

Sum of Cubes of First n Natural Numbers

The formula for the sum 1³ + 2³ + ... + n³ is [n(n + 1) ÷ 2]².

Sum of First n Odd Natural Numbers

The sum of the first n odd numbers (1 + 3 + 5 + ...) is always equal to n².

Sum of First n Even Natural Numbers

The sum of the first n even numbers (2 + 4 + 6 + ...) is given by n(n + 1).

Shortcut Trick

Side of rhombus = Perimeter ÷ 4 = 52 ÷ 4 = 13 cm.

Half of the given diagonal = 24 ÷ 2 = 12 cm.

Using Pythagorean Triplet (5, 12, 13), half of the other diagonal must be 5 cm.

Length of the other diagonal = 5 × 2 = 10 cm.

∴ The correct answer is 10 cm.

Alternate Method

Given: Perimeter = 52 cm, One diagonal (d₁) = 24 cm.

Formula Used: Side² = (d₁/2)² + (d₂/2)²

Calculations:

⇒ Side = Perimeter ÷ 4 = 52 ÷ 4 = 13 cm.

⇒ Let the other diagonal be d₂.

⇒ (13)² = (24 ÷ 2)² + (d₂ ÷ 2)²

⇒ 169 = (12)² + (d₂ ÷ 2)²

⇒ 169 = 144 + (d₂ ÷ 2)²

⇒ (d₂ ÷ 2)² = 169 − 144 = 25

⇒ d₂ ÷ 2 = √25 = 5

⇒ d₂ = 5 × 2 = 10 cm.

∴ The correct answer is 10 cm.

Additional Information

Area of Rhombus

The area of a rhombus can be calculated as Area = 1/2 × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.

Properties of Diagonals

The diagonals of a rhombus bisect each other at right angles (90°), forming four congruent right-angled triangles.

Side-Diagonal Relationship

A direct relationship between side (a) and diagonals is given by 4a² = d₁² + d₂².

Shortcut Trick

Relation: (d₁ + d₂)² = 4a² + 4 × Area

Given d₁ + d₂ = 46 cm and side a = 17 cm

⇒ 46² = 4 × 17² + 4 × Area

⇒ 2116 = 1156 + 4 × Area

⇒ 4 × Area = 960 ⇒ Area = 240 cm²

∴ The correct answer is 240 cm².

Alternate Method

Given:

Sum of diagonals (d₁ + d₂) = 46 cm

Side of the rhombus (a) = 17 cm

Formula Used:

1. 4a² = d₁² + d₂² (Relation between side and diagonals)

2. Area of rhombus = 1/2 × d₁ × d₂

Calculations:

⇒ d₁² + d₂² = 4 × (17)²

⇒ d₁² + d₂² = 4 × 289 = 1156

⇒ We know, (d₁ + d₂)² = d₁² + d₂² + 2d₁d₂

⇒ (46)² = 1156 + 2d₁d₂

⇒ 2116 = 1156 + 2d₁d₂

⇒ 2d₁d₂ = 2116 − 1156 = 960

⇒ d₁d₂ = 480

⇒ Area = 1/2 × 480 = 240 cm²

∴ The correct answer is 240 cm².

Additional Information

Properties of a Rhombus

All four sides of a rhombus are equal, and the diagonals bisect each other at 90° (perpendicularly).

Diagonal and Side Relation

The relation between the side 'a' and diagonals d₁, d₂ is given by 4a² = d₁² + d₂², which is derived from the Pythagoras theorem.

Area Formulas

Area of a rhombus = 1/2 × d₁ × d₂ OR Area = Base × Height.

Shortcut Trick

Convert all fractions to their simplest irreducible form: 3/4, 6/8 → 3/4, and 9/10.

Shortcut formula: LCM of Fractions = LCM of Numerators ÷ HCF of Denominators.

Numerators are 3 and 9 ⇒ LCM(3, 9) = 9.

Denominators are 4 and 10 ⇒ HCF(4, 10) = 2.

Required LCM = 9/2.

∴ The correct answer is 9/2.

Alternate Method

Given: The fractions are 3/4, 6/8, and 9/10.

Formula Used: LCM of fractions = [LCM of Numerators] ÷ [HCF of Denominators]

⇒ First, simplify the given fractions to their lowest terms: 3/4 remains 3/4, 6/8 becomes 3/4, and 9/10 remains 9/10.

⇒ Identification of terms: Numerators = 3, 3, 9; Denominators = 4, 4, 10.

⇒ Calculate the Least Common Multiple (LCM) of the Numerators: LCM(3, 3, 9) = 9.

⇒ Calculate the Highest Common Factor (HCF) of the Denominators: HCF(4, 4, 10) = 2.

⇒ Applying the formula: LCM = 9/2.

∴ The correct answer is 9/2.

Additional Information

HCF of Fractions

The Highest Common Factor of fractions is calculated as: HCF of Fractions = (HCF of Numerators) ÷ (LCM of Denominators).

Simplification Rule

Before calculating the LCM or HCF of any group of fractions, it is mandatory to reduce every fraction to its lowest terms (simplest form) to avoid incorrect results.

Fundamental Definitions

LCM is the simplest positive integer divisible by all numbers in a set, while HCF is the largest positive integer that divides all numbers in the set without leaving a remainder.

Shortcut Trick

Direct Property: Product of two numbers = HCF × LCM.

Required Product = 18 × 540

Required Product = 9720

∴ The correct answer is 9720.

Alternate Method

Given:

Highest Common Factor (HCF) of two numbers = 18

Least Common Multiple (LCM) of two numbers = 540

Formula Used:

Product of two numbers = HCF × LCM

Calculations:

⇒ Product = 18 × 540

⇒ Product = 18 × (500 + 40)

⇒ Product = (18 × 500) + (18 × 40)

⇒ Product = 9000 + 720

⇒ Product = 9720

∴ The correct answer is 9720.

Additional Information

Relationship for Two Numbers

For any two positive integers a and b, the product of the numbers is always equal to the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b).

HCF and LCM of Fractions

HCF of fractions = (HCF of Numerators) ÷ (LCM of Denominators) and LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators).

Co-prime Numbers

If two numbers are co-prime, their HCF is 1, and their LCM is simply the product of the two numbers.

Shortcut Trick

Loss Percentage = 40% = 2/5 (where 5 units is CP and 2 units is Loss).

Ratio of Selling Price = 5 − 2 = 3 units.

Given, 5 units = ₹4800 ⇒ 1 unit = ₹960.

Selling Price = 3 units = 3 × 960 = ₹2880.

∴ The correct answer is ₹2880.

Alternate Method

Given:

Cost Price (CP) of the article = ₹4800

Loss Percentage = 40%

Formula Used:

Selling Price (SP) = Cost Price × (100 − Loss%) / 100

Calculations:

⇒ Selling Price = 4800 × (100 − 40) / 100

⇒ Selling Price = 4800 × 60 / 100

⇒ Selling Price = 48 × 60

⇒ Selling Price = 2880

∴ The correct answer is ₹2880.

Additional Information

Profit Calculation

When the Selling Price is higher than the Cost Price, Profit = SP − CP.

Selling Price with Profit %

To find SP when profit percentage is given: SP = CP × (100 + Profit%) / 100.

Discount and Marked Price

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Shortcut Trick

If 30% of the eggs are rotten, then (100% − 30%) = 70% of the eggs are not rotten.

Calculate 70% of the total eggs directly:

⇒ 70% × 420 = 0.7 × 420 = 294

∴ The correct answer is 294 eggs.

Alternate Method

Given:

Total number of eggs = 420

Percentage of rotten eggs = 30%

Formula Used:

Number of not rotten eggs = Total Eggs − (Percentage of Rotten Eggs × Total Eggs ÷ 100)

Calculations:

⇒ Number of rotten eggs = 30% of 420

⇒ Rotten eggs = (30 ÷ 100) × 420 = 126

⇒ Number of not rotten eggs = Total Eggs − Rotten Eggs

⇒ Not rotten eggs = 420 − 126

⇒ Not rotten eggs = 294

∴ The correct answer is 294 eggs.

Additional Information

Percentage Complement Rule

If a certain part of a whole is x%, the remaining part is always (100 − x)% of the whole.

Percentage to Value Conversion

To find the absolute value from a percentage, use the formula: Value = (Percentage ÷ 100) × Total Base Value.

Fraction Equivalents

Common percentages can be simplified: 25% = 1/4, 50% = 1/2, 75% = 3/4, and 10% = 1/10.

Shortcut Trick

Ratio of Selling Price (SP) to Cost Price (CP) = 5 : 4.

Profit = 5 − 4 = 1 unit.

Profit % = (Profit ÷ CP) × 100.

Profit % = (1 ÷ 4) × 100 = 25%.

∴ The correct answer is 25 percent.

Alternate Method

Given: The ratio of the selling price (SP) of an article to the cost price (CP) of the article is 5 : 4.

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

⇒ Let the Cost Price (CP) be 4x.

⇒ Then, the Selling Price (SP) is 5x.

⇒ Profit = SP − CP = 5x − 4x = x.

⇒ Profit % = (Profit ÷ CP) × 100

⇒ Profit % = (x ÷ 4x) × 100

⇒ Profit % = 1/4 × 100 = 25%.

∴ The correct answer is 25 percent.

Additional Information

Loss Percentage

When SP < CP, Loss Percentage = [(CP − SP) ÷ CP] × 100.

Selling Price Formulas

SP = CP × (100 + Profit %) ÷ 100 or SP = CP × (100 − Loss %) ÷ 100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Shortcut Trick

Ratio of numbers = (3/5 x 30) : (1/4 x 80) = 18 : 20 = 9 : 10.

Difference between parts = 10 − 9 = 1 unit → 400.

Sum of numbers = 9 + 10 = 19 units → 19 x 400 = 7600.

Required Value = 25% of 7600 = 7600 ÷ 4 = 1900.

∴ The correct answer is 1900.

Alternate Method

Given: One-fourth of 80 percent of x = 3/5 of 30 percent of y. Difference = 400.

Formula: Percentage of a number = (Rate ÷ 100) x Number.

⇒ (1/4) x (80/100) x x = (3/5) x (30/100) x y

⇒ (20/100) x x = (18/100) x y

⇒ 20x = 18y

⇒ x/y = 18/20 = 9/10

⇒ Let numbers be 9k and 10k.

⇒ Difference = 10k − 9k = 1k = 400.

⇒ Sum = 9k + 10k = 19k = 19 x 400 = 7600.

⇒ 25 percent of sum = 7600 x (25/100) = 1900.

∴ The correct answer is 1900.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert percentages to fractions: 25% = 1/4, 20% = 1/5, 80% = 4/5, and 30% = 3/10.

Ratio and Proportionality

If x : y = a : b, then the difference is |a − b| parts and the sum is (a + b) parts. Value of 1 part = Actual Difference ÷ |a − b|.

Distributive Property of Percentages

P% of (x + y) = P% of x + P% of y. This property allows calculating the percentage of a total by summing individual percentage results.

Shortcut Trick

Ratio of Efficiency is the reciprocal of Time taken: 1/18 : 1/24 : 1/36.

Multiply by LCM (72) to get the ratio: 4 : 3 : 2.

Total efficiency parts = 4 + 3 + 2 = 9 parts.

P's share = (Efficiency of P ÷ Total Efficiency) × Total Wage.

P's share = (3 ÷ 9) × 7200 = 1/3 × 7200 = ₹2400.

∴ The correct answer is ₹2400.

Alternate Method

Given:

Time taken by R = 18 days

Time taken by P = 24 days

Time taken by G = 36 days

Total amount received = ₹7200

Formula Used:

When multiple people work for the same amount of time, their Wages are distributed in the ratio of their Efficiencies.

Calculations:

⇒ Ratio of Efficiency (R : P : G) = 4 : 3 : 2

⇒ Sum of Efficiency ratios = 4 + 3 + 2 = 9 units

⇒ 9 units = ₹7200

⇒ 1 unit = 7200 ÷ 9 = ₹800

⇒ P's share (3 units) = 3 × 800

⇒ P's share = ₹2400

∴ The correct answer is ₹2400.

Additional Information

Work and Wages Relationship

Wages are directly proportional to the Work Done. If time is constant, Wage ∝ Efficiency.

Efficiency and Time

Efficiency is inversely proportional to the Time taken to complete a task. Efficiency = Total Work ÷ Time.

Total Work Calculation

The Total Work is generally assumed as the LCM (Least Common Multiple) of the individual days to simplify efficiency calculations.

Shortcut Trick

Total hours for R = 12 × 4 = 48 hr.

Total hours for S = 6 × 8 = 48 hr.

Total hours together = (48 × 48) ÷ (48 + 48) = 24 hr.

Hours per day for 4 days = Total hours ÷ Days = 24 ÷ 4 = 6 hr.

∴ The correct answer is 6 hr.

Alternate Method

Given:

Work duration for R = 12 days × 4 hr = 48 hr.

Work duration for S = 6 days × 8 hr = 48 hr.

⇒ Total combined efficiency of R and S = 1 + 1 = 2 units/hr.

⇒ Total time required by R and S together = Total Work ÷ Combined Efficiency

⇒ Total time = 48 ÷ 2 = 24 hr.

⇒ They need to complete the work in 4 days.

⇒ Hours per day needed = 24 hr ÷ 4 days = 6 hr/day.

∴ The correct answer is 6 hr.

Additional Information

Combined Work Formula

If two people A and B can do a work in x and y hours respectively, they together take (x × y) ÷ (x + y) hours to finish it.

Man-Days-Hours (MDH) Relation

Total Work = Persons × Days × Hours per day. For constant work, M₁D₁H₁ = M₂D₂H₂.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete a specific task (Efficiency = 1 ÷ Time).

Shortcut Trick

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

Speed = 50 × (18/5)

Speed = 10 × 18 = 180 km/hr

∴ The correct answer is 180 km/hr.

Alternate Method

Given:

Speed of the train = 50 m/s

Formula Used:

Speed (km/hr) = Speed (m/s) × (3600 / 1000) = Speed (m/s) × (18 / 5)

Calculations:

⇒ Speed = 50 m/s

⇒ 1 m/s = (1/1000) km / (1/3600) hr

⇒ 1 m/s = 3600 / 1000 km/hr = 18 / 5 km/hr

⇒ Speed in km/hr = 50 × (18 / 5)

⇒ Speed in km/hr = 10 × 18

⇒ Speed in km/hr = 180 km/hr

∴ The correct answer is 180 km/hr.

Additional Information

km/hr to m/s Conversion

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

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, Average Speed = 2xy / (x + y).

Relative Speed

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

Shortcut Trick

Assume each equal distance is the LCM of speeds (10, 30, 60) = 60 km.

Total Distance = 3 × 60 = 180 km.

Total Time = (60 ÷ 10) + (60 ÷ 30) + (60 ÷ 60) = 6 + 2 + 1 = 9 hours.

Average Speed = Total Distance ÷ Total Time = 180 ÷ 9 = 20 km/hr.

∴ The correct answer is 20 km/hr.

Alternate Method

Given: Speeds of three equal parts of the journey are 10 km/hr, 30 km/hr, and 60 km/hr.

Formula Used: Average Speed = (3 × v₁ × v₂ × v₃) ÷ (v₁v₂ + v₂v₃ + v₃v₁)

Calculations:

⇒ Let the three equal distances be d each.

⇒ Total Distance = d + d + d = 3d

⇒ Total Time = (d ÷ 10) + (d ÷ 30) + (d ÷ 60)

⇒ Total Time = (6d + 2d + d) ÷ 60 = 9d ÷ 60 = 3d ÷ 20

⇒ Average Speed = (3d) ÷ (3d ÷ 20)

⇒ Average Speed = 3d × (20 ÷ 3d) = 20 km/hr

∴ The correct answer is 20 km/hr.

Additional Information

Average Speed for Two Equal Distances

When a journey is divided into two equal distances with speeds x and y, the Average Speed = 2xy ÷ (x + y).

Unit Conversion

To convert Speed from km/hr to m/s, multiply the value by 5 ÷ 18. To convert m/s to km/hr, multiply by 18 ÷ 5.

Constant Time Case

If a person travels for equal intervals of time at different speeds v₁ and v₂, the Average Speed is simply the arithmetic mean: (v₁ + v₂) ÷ 2.

Shortcut Trick

Let Cost Price (CP) = 100

Marked Price (MP) = 450% of 100 = 450

Selling Price (SP) = 100 ÷ 25% = 400

Discount % = (MP − SP) / MP × 100 = (50 / 450) × 100 = 11.11%

∴ The correct answer is 11.11 percent.

Alternate Method

Given:

Marked Price (MP) = 450% of Cost Price (CP)

Cost Price (CP) = 25% of Selling Price (SP)

Formula Used:

Discount = Marked Price − Selling Price

Discount Percentage = (Discount ÷ Marked Price) × 100

Calculations:

⇒ Let CP = 100x

⇒ MP = 450% of 100x = 450x

⇒ CP = 25% of SP ⇒ 100x = (25/100) × SP

⇒ SP = 100x × 4 = 400x

⇒ Discount = MP − SP = 450x − 400x = 50x

⇒ Discount % = (50x ÷ 450x) × 100

⇒ Discount % = (1 ÷ 9) × 100 = 11.111...

∴ The correct answer is 11.11 percent.

Additional Information

Mark-up Percentage

It is the percentage by which the Cost Price is increased to reach the Marked Price. Formula: Mark-up % = (MP − CP) ÷ CP × 100.

Profit and Discount Relation

The relationship between CP and MP using Profit % and Discount % is: MP ÷ CP = (100 + Profit %) ÷ (100 − Discount %).

Successive Discounts

If two discounts d₁ and d₂ are given, the Equivalent Discount = d₁ + d₂ − (d₁ × d₂) ÷ 100.

Shortcut Trick

Convert percentage discounts into ratios: 20% = 1/5 and 25% = 1/4.

Initial Marked Price (MP) to Selling Price (SP) ratios: 5 : 4 and 4 : 3.

Combined Ratio = (5 × 4) : (4 × 3) = 20 : 12 or 5 : 3.

Given 3 units = Rs. 18000 ⇒ 1 unit = Rs. 6000. MP (5 units) = 5 × 6000 = Rs. 30000. ∴ The correct answer is Rs. 30000.

Alternate Method

Given: Final Selling Price (SP) = Rs. 18000, 1^st Discount (d₁) = 20%, 2^nd Discount (d₂) = 25%.

Formula Used: Final SP = Marked Price × (100 − d₁)/100 × (100 − d₂)/100

⇒ 18000 = MP × (100 − 20)/100 × (100 − 25)/100

⇒ 18000 = MP × (80/100) × (75/100)

⇒ 18000 = MP × (4/5) × (3/4)

⇒ 18000 = MP × (3/5)

⇒ MP = (18000 × 5) ÷ 3

⇒ MP = 6000 × 5

⇒ MP = Rs. 30000

∴ The correct answer is Rs. 30000.

Additional Information

Single Equivalent Discount

For two successive discounts a% and b%, the effective discount is (a + b − ab/100)%. Here, 20 + 25 − (20 × 25 / 100) = 45 − 5 = 40%.

Marked Price (MP) Relation

If SP and discount % are known, MP = [SP ÷ (100 − Discount%)] × 100. For successive discounts, multiply the factors for each step.

Profit and Markup

Relation between CP, MP, and Profit: MP/CP = (100 + Profit%)/(100 − Discount%). This helps find CP when Profit and Discount percentages are given.

Shortcut Trick

Marked Price = ₹4000

Price after first discount of 25% = 4000 − (25% of 4000) = ₹3000

Final Selling Price = ₹2400

Second discount amount = 3000 − 2400 = ₹600

Value of A = (600 ÷ 3000) × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Marked Price (MP) = ₹4000

First discount = 25%

Second discount = A%

Final Selling Price (SP) = ₹2400

Formula used:

SP = MP × (100 − d₁)/100 × (100 − d₂)/100

Calculations:

⇒ Price after first discount = 4000 × (100 − 25) ÷ 100

⇒ 4000 × 75/100 = ₹3000

⇒ Final SP = 3000 × (100 − A) ÷ 100

⇒ 2400 = 3000 × (100 − A) ÷ 100

⇒ 2400 ÷ 30 = 100 − A

⇒ 80 = 100 − A

⇒ A = 100 − 80

⇒ A = 20

∴ The correct answer is 20%.

Additional Information

Successive Discount Formula

The single equivalent discount for two successive discounts of x% and y% is given by [x + y − (xy ÷ 100)]%.

Relationship between MP and SP

The final selling price can be directly calculated as SP = MP × (1 − d₁/100) × (1 − d₂/100) × ... × (1 − d_n/100).

Effective Discount Rate

Total Discount % = [(Marked Price − Final Selling Price) ÷ Marked Price] × 100.