Quantitative Aptitude PYQs

Shortcut Trick

Solve Division and Multiplication first: 27 ÷ 3 = 9 and 19 × 1 = 19.

The expression simplifies to: 94 + 36 − 9 + 33 + 19 − 29.

Combine all positive and negative terms separately: (94 + 36 + 33 + 19) − (9 + 29).

Result: 182 − 38 = 144.

∴ The correct answer is 144.

Alternate Method

Follow the BODMAS rule to solve the expression: 94 + 36 − (27 ÷ 3) + 33 + 19 × 1 − 29.

Step 1: Solve the operation inside the bracket (Division).

⇒ 94 + 36 − 9 + 33 + 19 × 1 − 29

Step 2: Solve the Multiplication.

⇒ 94 + 36 − 9 + 33 + 19 − 29

Step 3: Perform Addition from left to right.

⇒ 130 − 9 + 33 + 19 − 29

⇒ 121 + 33 + 19 − 29

⇒ 154 + 19 − 29

⇒ 173 − 29

Step 4: Perform Subtraction.

⇒ 144

∴ The correct answer is 144.

Additional Information

BODMAS Rule

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

Precedence of Operations

Operations like Division and Multiplication have the same precedence and are solved from left to right, as are Addition and Subtraction.

VBODMAS Rule

This is an extension where V stands for Vinculum or bar bracket, which is solved before all other brackets.

Shortcut Trick

The time when all bells ring together again is the LCM of their ringing intervals.

Intervals: 18, 24, and 30 seconds.

LCM(18, 24, 30) = 360 seconds.

Time in minutes = 360 ÷ 60 = 6 min.

∴ The correct answer is 6 min.

Alternate Method

Given:

Interval of Bell 1 = 18 seconds

Interval of Bell 2 = 24 seconds

Interval of Bell 3 = 30 seconds

Starting time = 10:00:00 AM

Calculations:

⇒ To find the time when they ring together again, calculate the Least Common Multiple (LCM).

⇒ Prime factorization of 18 = 2 × 3 × 3 = 2¹ × 3²

⇒ Prime factorization of 24 = 2 × 2 × 2 × 3 = 2³ × 1¹

⇒ Prime factorization of 30 = 2 × 3 × 5 = 2¹ × 3¹ × 5¹

⇒ LCM = (Highest power of each prime factor) = 2³ × 3² × 5¹

⇒ LCM = 8 × 9 × 5 = 360 seconds

⇒ Convert seconds to minutes: Time = 360 ÷ 60

⇒ Time = 6 minutes

∴ The correct answer is 6 min.

Additional Information

LCM and Periodic Events

For any events occurring at regular intervals (like bells, traffic lights, or runners), the first time they coincide after starting together is the LCM of their individual time periods.

Relationship between HCF and LCM

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

Time Conversion Rules

To convert seconds to minutes, divide by 60. To convert minutes to hours, divide by 60. To convert hours to seconds, multiply by 3600 (60 × 60).

Shortcut Trick

Identify the pattern of denominators: 3 = 1 × 3, 15 = 3 × 5, 35 = 5 × 7, 63 = 7 × 9.

The difference between factors in each term is constant (d = 2).

Shortcut formula: Sum = (Number of terms) ÷ (First factor × Last factor)

Here, Number of terms = 4, First factor = 1, Last factor = 9.

Sum = 4 ÷ (1 × 9) = 4/9.

∴ The correct answer is 4/9.

Alternate Method

Given Expression: 1/3 + 1/15 + 1/35 + 1/63

Formula Used: 1/[n × (n+d)] = (1/d) × [1/n − 1/(n+d)]

⇒ 1/(1 × 3) + 1/(3 × 5) + 1/(5 × 7) + 1/(7 × 9)

⇒ (1/2) × [1/1 − 1/3] + (1/2) × [1/3 − 1/5] + (1/2) × [1/5 − 1/7] + (1/2) × [1/7 − 1/9]

⇒ (1/2) × [1/1 − 1/3 + 1/3 − 1/5 + 1/5 − 1/7 + 1/7 − 1/9]

⇒ (1/2) × [1 − 1/9]

⇒ (1/2) × [8/9]

⇒ 4/9

∴ The correct answer is 4/9.

Additional Information

Telescoping Series

A telescoping series is a series where the partial sums eventually only have a fixed number of terms after most terms cancel out.

General Sum Formula

For any series 1/(a₁×a₂) + 1/(a₂×a₃) + ... + 1/(a_n−1×a_n) where a_i forms an AP with common difference d: Sum = (1/d) × [1/First − 1/Last].

Partial Fraction Decomposition

It is the process of breaking down a complex fraction into a sum of simpler fractions, which is the foundational logic behind solving rational series.

Shortcut Trick

Apply the algebraic identity: (a − b)² + 4ab = (a + b)²

Here, a = 2.85 and b = 1.15.

⇒ Result = (2.85 + 1.15)²

⇒ Result = (4.00)² = 16

∴ The correct answer is 16.

Alternate Method

Given: (2.85 − 1.15)² + 4 × 2.85 × 1.15

Simplification Steps:

⇒ First, solve the subtraction inside the bracket: (1.70)² + 4 × 2.85 × 1.15

⇒ Calculate the square: 1.70 × 1.70 = 2.89

⇒ Calculate the multiplication part: 4 × 2.85 × 1.15 = 11.4 × 1.15 = 13.11

⇒ Add the two results: 2.89 + 13.11

⇒ Sum = 16.00

∴ The correct answer is 16.

Additional Information

Relation between Square Identities

The sum and difference of squares are related by: (a + b)² − (a − b)² = 4ab.

Identity for Sum of Squares

Adding the identities (a + b)² and (a − b)² results in: (a + b)² + (a − b)² = 2(a² + b²).

BODMAS Rule

Always prioritize Brackets, followed by Orders (powers/roots), then Division/Multiplication, and finally Addition/Subtraction.

Shortcut Trick

Directly calculate square roots: √196 = 14, √49 = 7, and √81 = 9.

Solve for x using BODMAS: 14 ÷ 7 + 9 = 2 + 9 = 11.

Calculate the required value 2x: 2 × 11 = 22.

∴ The correct answer is 22.

Alternate Method

Given:

x = √196 ÷ √49 + √81

Calculation:

⇒ x = 14 ÷ 7 + 9 (Since 14² = 196, 7² = 49, and 9² = 81)

⇒ x = 2 + 9

⇒ x = 11

Now, find the value of 2x:

⇒ 2x = 2 × 11

⇒ 2x = 22

∴ The correct answer is 22.

Additional Information

BODMAS Rule

It specifies the order of operations: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

Perfect Squares

Numbers that are the result of multiplying an integer by itself. For example, 14 × 14 = 196 and 9 × 9 = 81.

Square Root Property

For non-negative numbers, √(a ÷ b) = √a ÷ √b. This allows for simplifying divisions involving radicals separately.

Shortcut Trick

Approximate the cube root of the product to find the middle number: √³315 ≈ 6.8.

The middle odd number near 6.8 is 7.

Consecutive odd numbers are 5, 7, and 9.

Sum = 5 + 7 + 9 = 21.

∴ The correct answer is 21.

Alternate Method

Given: The product of three consecutive odd numbers is 315.

Formula Used: Product of numbers = n₁ × n₂ × n₃

⇒ Factorize 315 into its prime factors: 315 = 5 × 63

⇒ 315 = 5 × 7 × 9

⇒ The numbers are identified as 5, 7, and 9 which are consecutive odd integers.

⇒ Required Sum = 5 + 7 + 9

⇒ Required Sum = 21

∴ The correct answer is 21.

Additional Information

Consecutive Odd/Even Numbers

Any sequence of consecutive odd or even numbers has a common difference of 2. If the first number is x, the next numbers are x + 2, x + 4, etc.

Average of Consecutive Numbers

For an odd count of consecutive numbers, the middle term is always the arithmetic mean (average) of the series.

Sum of Odd Numbers

The sum of the first n odd natural numbers starting from 1 is always n².

Shortcut Trick

The expression is in the form of a² + b² + 2ab, which equals (a + b)².

Here, a = 150 and b = 250.

⇒ (150 + 250)² = 400².

⇒ 400 × 400 = 160000.

∴ The correct answer is 160000.

Alternate Method

Given Expression: (150 × 150 + 250 × 250 + 2 × 150 × 250)

This is a simplification problem involving the expansion of a binomial square.

Formula Used: (a + b)² = a² + b² + 2ab

⇒ a² = 150 × 150 = 22500

⇒ b² = 250 × 250 = 62500

⇒ 2ab = 2 × 150 × 250 = 75000

⇒ Result = 22500 + 62500 + 75000

⇒ Result = 85000 + 75000

⇒ Result = 160000

∴ The correct answer is 160000.

Additional Information

Square of Sum Identity

The identity (a + b)² = a² + 2ab + b² is used to simplify the sum of squares and their product quickly.

Square of Difference Identity

Similarly, (a − b)² = a² − 2ab + b² is used when the middle term is subtracted.

Difference of Two Squares

The formula a² − b² = (a − b)(a + b) is vital for factoring expressions and simplifying divisions.

Calculation Shortcut for Squares

When squaring a number ending in 0, square the non-zero part and append double the number of zeros (e.g., 40² = 1600).

Shortcut Trick

Observe that each number in the numerator is exactly 10 times the corresponding number in the denominator (e.g., 4.1 = 0.41 × 10).

Since every term is squared, the numerator becomes 10² = 100 times the denominator.

The entire fraction inside the root simplifies to 100.

The value of the expression is √100 = 10.

∴ The correct answer is 10.

Alternate Method

Given: √(((4.1)² + (41.1)² + (411.1)²) / ((0.41)² + (4.11)² + (41.11)²))

Method: Factor out the common multiple from the numerator terms to match the denominator.

⇒ √(((10 × 0.41)² + (10 × 4.11)² + (10 × 41.11)²) / ((0.41)² + (4.11)² + (41.11)²))

⇒ √((10² × (0.41)² + 10² × (4.11)² + 10² × (41.11)²) / ((0.41)² + (4.11)² + (41.11)²))

⇒ √((100 × [(0.41)² + (4.11)² + (41.11)²]) / ((0.41)² + (4.11)² + (41.11)²))

⇒ √100

⇒ 10

∴ The correct answer is 10.

Additional Information

Power of a Product Rule

For any numbers a and b, (a × b)ⁿ = aⁿ × bⁿ. In this problem, (10 × x)² = 100x² was used to factor out the constant.

Decimal Point Shift

Multiplying a decimal number by 10 shifts the decimal point one place to the right, while dividing by 10 shifts it one place to the left.

Square Root of a Fraction

The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator: √(a/b) = √a / √b.

Shortcut Trick

Recognize the standard Pythagorean triplet: (8, 15, 17).

Since the diagonal (hypotenuse) is 17 cm and the length is 15 cm, the breadth must be 8 cm.

Perimeter = 2 × (Length + Breadth) = 2 × (15 + 8).

Perimeter = 2 × 23 = 46 cm.

∴ The correct answer is 46 cm.

Alternate Method

Given:

Length (L) = 15 cm

Diagonal (D) = 17 cm

Formula Used:

In a rectangle, Breadth (B) = √(Diagonal² − Length²)

Perimeter (P) = 2 × (Length + Breadth)

⇒ B² = D² − L²

⇒ B² = 17² − 15²

⇒ B² = 289 − 225

⇒ B² = 64

⇒ B = √64 = 8 cm

⇒ Perimeter = 2 × (15 + 8)

⇒ Perimeter = 2 × 23 = 46 cm

∴ The correct answer is 46 cm.

Additional Information

Pythagorean Triplets

Sets of three positive integers a, b, and c such that a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Area of a Rectangle

The total space occupied by the rectangle is calculated as Length × Breadth.

Properties of Rectangle Diagonals

The diagonals of a rectangle are equal in length and bisect each other at the point of intersection.

Shortcut Trick

Identify the algebraic identity: 2(a² + b²) − (a − b)² = (a + b)².

Let a = 530 and b = 270.

The expression simplifies to: (530 + 270)².

⇒ 800² = 640000.

∴ The correct answer is 640000.

Alternate Method

Given: a = 530, b = 270

Formula Used: Expansion of squares and basic arithmetic.

⇒ 2[(530)² + (270)²] − (530 − 270)²

⇒ 2[280900 + 72900] − (260)²

⇒ 2[353800] − 67600

⇒ 707600 − 67600

⇒ 640000

∴ The correct answer is 640000.

Additional Information

Algebraic Identities

The identity 2(a² + b²) = (a + b)² + (a − b)² is derived from adding the expansions of (a + b)² and (a − b)².

Square of Binomial

(a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab are fundamental tools for simplifying numerical expressions.

BODMAS Rule

Always solve terms inside Brackets first, followed by Orders (powers/roots), then Division/Multiplication, and finally Addition/Subtraction.

Shortcut Trick

Average of 5 days = ₹120

Net deviation from average must be 0.

Deviations: (50−120), (105−120), (95−120), (160−120) ⇒ −70, −15, −25, +40

Sum of deviations = −70 − 15 − 25 + 40 = −70

5^th day expenditure = 120 + 70 = 190

∴ The correct answer is ₹190.

Alternate Method

Given:

Average expenditure for 5 days = ₹120

Expenditure for first 4 days = ₹50, ₹105, ₹95, ₹160

Formula Used:

Total = Average × Number of observations

Calculations:

⇒ Total expenditure for 5 days = 120 × 5 = 600

⇒ Sum of expenditure for first 4 days = 50 + 105 + 95 + 160

⇒ Sum of 4 days = 410

⇒ 5^th day expenditure = Total expenditure − Sum of 4 days

⇒ 5^th day expenditure = 600 − 410 = 190

∴ The correct answer is ₹190.

Additional Information

Arithmetic Mean

The average or mean is calculated by dividing the sum of all values by the total number of values: Mean = (Σx_i) ÷ n.

Deviation Concept

The sum of deviations of all observations from their arithmetic mean is always zero: Σ(x_i − Mean) = 0.

Impact of Constant on Average

If every observation is increased or decreased by a constant 'k', the new average also increases or decreases by 'k'.

Shortcut Trick

The difference between Cost Price (CP) and Selling Price (SP) represents the Profit amount.

Given Profit% = 9% and the difference is ₹252.

Equating percentage to value: 9% → ₹252.

Calculating 100% (Cost Price): (252 ÷ 9) × 100 = 28 × 100 = ₹2800.

∴ The correct answer is ₹2800.

Alternate Method

Given:

Difference (SP − CP) = ₹252

Profit % = 9%

Formula Used:

Profit = (Profit % ÷ 100) × Cost Price (CP)

Calculations:

⇒ Profit = SP − CP = 252

⇒ 9% of CP = 252

⇒ (9 ÷ 100) × CP = 252

⇒ CP = (252 × 100) ÷ 9

⇒ CP = 28 × 100

⇒ CP = ₹2800

∴ The correct answer is ₹2800.

Additional Information

Profit and Loss Relationship

Profit occurs when Selling Price (SP) > Cost Price (CP). Profit = SP − CP. Loss occurs when CP > SP. Loss = CP − SP.

Percentage Calculation Base

Profit % and Loss % are always calculated on the Cost Price unless mentioned otherwise in the question. Formula: Profit % = (Profit ÷ CP) × 100.

Selling Price Formula

To find SP directly: SP = CP × (100 + Profit %) ÷ 100 or SP = CP × (100 − Loss %) ÷ 100.

Shortcut Trick

Find the effective percentage: (40 × 60) ÷ 100 = 24%.

Calculate 24% of the total value 6800.

⇒ 24 × 68 = 1632.

∴ The correct answer is 1632.

Alternate Method

Given:

Initial Value = 6800

First Percentage = 60%

Second Percentage = 40%

Calculations:

⇒ First, determine 60% of 6800:

⇒ (60 ÷ 100) × 6800 = 60 × 68 = 4080

⇒ Now, find 40% of the resultant 4080:

⇒ (40 ÷ 100) × 4080 = 40 × 40.8 = 1632

∴ The correct answer is 1632.

Additional Information

Compound Percentage Application

Finding a% of b% of a quantity is equivalent to finding (a × b / 100)% of that quantity. For example, 40% of 60% is 24%.

Fractional Equivalents

Simplifying percentages into fractions can speed up calculations: 40% = 2/5 and 60% = 3/5. Thus, (2/5) × (3/5) × 6800 = (6/25) × 6800 = 1632.

Percentage Change vs. Value

Always distinguish between a percentage of a percentage (multiplicative) and a percentage increase/decrease (additive/subtractive).

Shortcut Trick

Ratio of CP : SP = 3 : 5

Consider CP = 3 units and SP = 5 units.

Profit = SP − CP = 5 − 3 = 2 units.

Ratio of Profit : CP = 2 : 3.

∴ The correct answer is 2 : 3.

Alternate Method

Given:

Ratio of Cost Price (CP) to Selling Price (SP) = 3 : 5

Formula Used:

Profit = Selling Price − Cost Price

Calculations:

⇒ Let the Cost Price of the article be 3x.

⇒ Then the Selling Price of the article is 5x.

⇒ Profit = Selling Price − Cost Price

⇒ Profit = 5x − 3x = 2x

⇒ We need to find the ratio of Value of Profit to Cost Price.

⇒ Required Ratio = 2x : 3x

⇒ Required Ratio = 2 : 3

∴ The correct answer is 2 : 3.

Additional Information

Profit Percentage

Profit % = (Profit ÷ Cost Price) × 100. In this case, Profit % = (2 ÷ 3) × 100 = 66.66%.

Loss Percentage

Loss occurs when CP > SP. Loss % = (Loss ÷ Cost Price) × 100, where Loss = CP − SP.

Marked Price and Discount

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

Shortcut Trick

Let the total number of employees be 100%.

Matriculates = 20%, so Remaining = 80%.

Graduates = 40% of 80% = 32%.

Post-graduates = 80% − 32% = 48%.

Given 48% = 144 ⇒ 1% = 3 employees.

∴ The correct answer is 60 employees.

Alternate Method

Given:

Matriculates = 20% of Total

Graduates = 40% of (Total − Matriculates)

Post-graduates = 144

Calculations:

⇒ Let Total Employees = x

⇒ Employees after matriculates = x − 0.20x = 0.80x

⇒ Post-graduates = (100% − 40%) of 0.80x

⇒ 144 = 0.60 × 0.80x

⇒ 144 = 0.48x

⇒ x = 144 ÷ 0.48

⇒ x = 300

⇒ Number of Matriculates = 20% of 300

⇒ Matriculates = 0.20 × 300 = 60

∴ The correct answer is 60 employees.

Additional Information

Successive Percentage Reduction

When values are reduced step-by-step from the remainder, the final percentage is the product of the remaining multipliers: Final % = (1 − r₁) × (1 − r₂) × 100.

Base Value Concept

Always identify the base for each percentage. Here, 40% is calculated on the 80% remaining, not on the original 100% total.

Fraction Conversion

20% = 1/5 and 40% = 2/5. Total × (4/5) × (3/5) = 144 can also be used for faster calculation.

Shortcut Trick

Work completed in 6 days = 30%

Work completed in 1 day = 30% ÷ 6 = 5%

Work completed in 10 days = 5% × 10 = 50%

∴ The correct answer is 50%.

Alternate Method

Given:

Work done by A in 6 days (W₁) = 30%

Time period 1 (T₁) = 6 days

Time period 2 (T₂) = 10 days

Formula Used:

Work (W) = Efficiency (E) × Time (T)

Calculations:

⇒ Efficiency of A = W₁ ÷ T₁

⇒ Efficiency of A = 30% ÷ 6 = 5% per day

⇒ Work completed in 10 days (W₂) = Efficiency × T₂

⇒ W₂ = 5% × 10

⇒ W₂ = 50%

∴ The correct answer is 50%.

Additional Information

Rate of Work

Efficiency or rate of work is the amount of work completed in a unit of time (e.g., 1 day or 1 hour). Formula: Efficiency = Total Work ÷ Total Time.

Direct Proportionality

When efficiency is constant, work done is directly proportional to the time taken. If time increases, work done increases in the same ratio: W₁/T₁ = W₂/T₂.

Total Work Completion Time

To find the time taken for 100% work, use the unitary method: Total Time = (Current Time ÷ Current Work %) × 100. In this case: (6 ÷ 30) × 100 = 20 days.

Shortcut Trick

Efficiency of (Q + R) is 5 times that of P.

Since Work = Efficiency × Time, for the same work, Time is inversely proportional to Efficiency.

Ratio of Efficiency [(Q + R) : P] = 5 :

1. Ratio of Time [(Q + R) : P] = 1 : 5.

Given, Time for (Q + R) = 45 days.

Time for P = 5 × 45 = 225 days.

∴ The correct answer is 225 days.

Alternate Method

Given:

(Q + R) = 5P ⇒ (P + Q + R) = 6P

(P + R) = 3Q ⇒ (P + Q + R) = 4Q

Time taken by (Q + R) = 45 days

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Let the efficiency of P be 1 unit/day.

⇒ Then, efficiency of (Q + R) = 5 × 1 = 5 units/day.

⇒ Total Work = Efficiency of (Q + R) × Time taken by (Q + R)

⇒ Total Work = 5 × 45 = 225 units.

⇒ Time taken by P alone = Total Work ÷ Efficiency of P

⇒ Time taken by P alone = 225 ÷ 1 = 225 days.

∴ The correct answer is 225 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiencies of A and B is x : y, then the ratio of time taken is y :

x. Total Work Formula

Total Work = Number of days × Efficiency. This remains constant for different individuals or groups performing the same task.

Combined Efficiency

When individuals work together, their individual efficiencies are added to find the combined rate of work per unit time.

Shortcut Trick

Convert Speed directly to m/s: 18 × (5/18) = 5 m/s.

Convert Time to seconds: 8 min × 60 = 480 seconds.

Bridge Length = Speed × Time = 5 × 480 = 2400 metres.

∴ The correct answer is 2400 m.

Alternate Method

Given:

Speed of the boy = 18 km/hr

Time taken to cross = 8 min

Formula Used:

Distance (Length) = Speed × Time

Calculations:

⇒ Step 1: Convert Speed from km/hr to m/s

⇒ Speed = 18 × (5/18) = 5 m/s

⇒ Step 2: Convert Time from minutes to seconds

⇒ Time = 8 × 60 = 480 seconds

⇒ Step 3: Calculate the Length of the bridge

⇒ Length = 5 × 480 = 2400 metres

∴ The correct answer is 2400 m.

Additional Information

Unit Conversion Rules

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

Basic Speed Formula

Distance = Speed × Time. Ensure all units are consistent (e.g., if distance is in metres, time must be in seconds and speed in m/s).

Average Speed

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

Shortcut Trick

Distance of bus = 80 × 10 = 800 km

Distance of train = 800 + 100 = 900 km

Time taken by train = 10 + 5 = 15 hr

Speed of train = 900 ÷ 15 = 60 km/hr

∴ The correct answer is 60 km/hr.

Alternate Method

Given:

Speed of bus = 80 km/hr

Time taken by bus = 10 hr

Extra distance by train = 100 km

Extra time taken by train = 5 hr

Formula Used:

Distance = Speed × Time

Speed = Distance ÷ Time

⇒ Distance covered by the bus = 80 × 10 = 800 km

⇒ Distance covered by the train = 800 + 100 = 900 km

⇒ Time taken by the train = 10 + 5 = 15 hr

⇒ Speed of the train = 900 ÷ 15 = 60 km/hr

∴ The correct answer is 60 km/hr.

Additional Information

Average Speed

It is the total distance traveled divided by the total time taken. Average Speed = (Total Distance) ÷ (Total Time).

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. When they move in opposite directions, relative speed = S₁ + S₂.

Speed Unit Conversion

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

Shortcut Trick

A 20% discount means the Selling Price (SP) is 80% of the Marked Price (MP).

Ratio of SP : MP = 80 : 100 = 4 : 5.

Check ratios: 2000 : 2500 = 20 : 25 = 4 : 5.

∴ The correct answer is Selling price = ₹2000 and Marked price = ₹2500.

Alternate Method

Given: Selling Price (SP) = ₹2000 and Marked Price (MP) = ₹2500.

Formula Used: Discount % = [(MP − SP) ÷ MP] × 100

⇒ Discount = MP − SP

⇒ Discount = 2500 − 2000 = ₹500

⇒ Discount % = (500 ÷ 2500) × 100

⇒ Discount % = (1 ÷ 5) × 100 = 20%

∴ The correct answer is Selling price = ₹2000 and Marked price = ₹2500.

Additional Information

Successive Discounts

When two discounts d₁% and d₂% are given, the equivalent single discount is [d₁ + d₂ − (d₁ × d₂) ÷ 100]%.

Marked Price and Markup Percentage

Markup percentage is the percentage by which the Cost Price (CP) is increased to reach the MP. Markup % = [(MP − CP) ÷ CP] × 100.

Relation between CP and MP

The relationship between CP, MP, Profit%, and Discount% is given by MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).