Quantitative Aptitude PYQs

Shortcut Trick

Solve using the BODMAS rule by prioritising brackets and multiplication.

Calculate Bracket: (41 + 23) = 64.

Calculate Multiplication: 64 × 2 = 128.

Final expression: 56 + 74 − 52 + 128 − 96 = 110.

∴ The correct answer is 110.

Alternate Method

Given: 56 + 74 − 52 + (41 + 23) × 2 − 96

Rule Used: BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

⇒ 56 + 74 − 52 + (64) × 2 − 96

⇒ 56 + 74 − 52 + 128 − 96

⇒ (56 + 74 + 128) − (52 + 96)

⇒ 258 − 148

⇒ 110

∴ The correct answer is 110.

Additional Information

The BODMAS Rule

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

Left-to-Right Rule

When operators of the same priority level appear (like + and −), solve the expression from left to right to maintain accuracy.

Shortcut Trick

Solve the expression using the BODMAS rule by identifying operations in order.

72 + 38 − (96 ÷ 12) + 29 of 2 − 14

⇒ 72 + 38 − 8 + 58 − 14

⇒ 110 + 50 − 14

⇒ 160 − 14 = 146

∴ The correct answer is 146.

Alternate Method

Given:

72 + 38 − (96 ÷ 12) + 29 of 2 − 14

Formula Used:

Apply the VBODMAS rule (Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction).

Calculations:

⇒ 72 + 38 − 8 + 29 of 2 − 14 (Solving Bracket: 96 ÷ 12 = 8)

⇒ 72 + 38 − 8 + 58 − 14 (Solving Of: 29 × 2 = 58)

⇒ 110 − 8 + 58 − 14 (Solving Addition: 72 + 38 = 110)

⇒ 102 + 58 − 14 (Solving Subtraction: 110 − 8 = 102)

⇒ 160 − 14 (Solving Addition: 102 + 58 = 160)

⇒ 146 (Solving Subtraction: 160 − 14 = 146)

∴ The correct answer is 146.

Additional Information

VBODMAS Rule

The order of priority is Vinculum (bar), Brackets (), Of (multiplication), Division (÷), Multiplication (×), Addition (+), and Subtraction (−).

'Of' Operator

The 'of' operator is treated as multiplication but must be performed before Division and Multiplication according to standard mathematical hierarchy.

Left-to-Right Rule

When operations of the same priority (like Addition and Subtraction) appear, it is best to solve them from left to right to avoid confusion.

Shortcut Trick

Separate Whole Numbers and Fractions: (7 + 9 − 5) + (2/7 + 1/3 − 3/4)

Integer part: 11

Fraction part: LCM(7, 3, 4) = 84

Fractional sum: (24 + 28 − 63) / 84 = −11/84

Combine: 11 − 11/84 = 10 + (1 − 11/84) = 10(73/84)

∴ The correct answer is 10(73/84).

Alternate Method

Given: 7(2/7) + 9(1/3) − 5(3/4)

Method: Mixed fraction decomposition into Integer and Proper Fraction.

⇒ (7 + 2/7) + (9 + 1/3) − (5 + 3/4) ⇒ (7 + 9 − 5) + (2/7 + 1/3 − 3/4) ⇒ 11 + [(2 × 12 + 1 × 28 − 3 × 21) / 84] ⇒ 11 + [(24 + 28 − 63) / 84] ⇒ 11 + [−11 / 84] ⇒ 11 − 11/84 ⇒ 10 + 1 − 11/84 ⇒ 10 + (84 − 11) / 84 ⇒ 10 + 73/84 ⇒ 10(73/84)

∴ The correct answer is 10(73/84).

Additional Information

Mixed Fractions

A mixed fraction is the sum of a non-zero integer and a proper fraction. For any mixed fraction A(b/c), it is calculated as (A × c + b) / c.

LCM of Denominators

When performing addition or subtraction of fractions, a common denominator must be established using the Least Common Multiple (LCM) of the given denominators.

Negative Fractional Parts

If the sum of fractional parts is negative, borrow 1 from the integer part (1 = c/c) to make the resulting fractional part positive.

Shortcut Trick

Solve the square roots first: √0.09 = 0.3 and √0.36 = 0.6.

Substitute back: (0.3/0.6) × (0.4/0.6) × (1.8/0.6).

Simplify each fraction: (1/2) × (2/3) × 3.

Multiply the simplified values: 0.5 × 2 = 1.

∴ The correct answer is 1.

Alternate Method

Given: (√0.09/0.6) × (0.4/√0.36) × (1.8/√0.36)

Method: BODMAS and Square Root simplification

⇒ Step 1: Find the square roots of the decimals.

⇒ √0.09 = √(9/100) = 3/10 = 0.3

⇒ √0.36 = √(36/100) = 6/10 = 0.6

⇒ Step 2: Substitute values into the expression.

⇒ Result = (0.3/0.6) × (0.4/0.6) × (1.8/0.6)

⇒ Step 3: Simplify the ratios.

⇒ Result = (1/2) × (2/3) × 3

⇒ Result = (1/2) × 2 = 1

∴ The correct answer is 1.

Additional Information

Square Root of Decimals

To find the square root of a decimal, express it as a fraction (e.g., 0.09 = 9/100) and then take the square root of both numerator and denominator.

BODMAS Rule

Always follow the BODMAS order: Brackets, Orders (powers/roots), Division and Multiplication (left to right), and Addition and Subtraction.

Fraction Simplification

When dealing with decimal fractions, you can remove decimals by multiplying the numerator and denominator by 10ⁿ, where n is the number of decimal places.

Shortcut Trick

Solve the expression under the square root by calculating the square and products first.

18² = 324, 8 × 8 = 64, and 5 × 22 = 110.

Combine the results: 324 + 64 − 110 + 11 = 289.

The square root of 289 is 17.

∴ The correct answer is 17.

Alternate Method

Given: √(18² + 8 × 8 − 5 × 22 + 11)

Formula Used: BODMAS Rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

⇒ √(324 + 64 − 110 + 11)

⇒ √(388 − 110 + 11)

⇒ √(278 + 11)

⇒ √289

⇒ 17

∴ The correct answer is 17.

Additional Information

BODMAS Rule

The BODMAS acronym defines the correct sequence for solving mathematical operations: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

Perfect Squares

Memorizing perfect squares from 1 to 30 (e.g., 17² = 289, 18² = 324) is crucial for improving speed in simplification and quantitative aptitude sections.

Square Root Calculation

The square root (√) is the inverse operation of squaring a number; if x² = y, then √y = x.

Shortcut Trick

Second diagonal (d₂) = (2 × 216) ÷ 18 = 24 cm.

Half-diagonals are 9 cm and 12 cm.

Using the Pythagorean triplet (3, 4, 5) scaled by 3 → (9, 12, 15).

Therefore, the side of the rhombus = 15 cm.

Perimeter = 4 × 15 = 60 cm.

∴ The correct answer is 60 cm.

Alternate Method

Given: Area of rhombus = 216 cm² and one diagonal (d₁) = 18 cm.

Formula: Area = (1/2) × d₁ × d₂

⇒ 216 = (1/2) × 18 × d₂

⇒ 216 = 9 × d₂

⇒ d₂ = 216 ÷ 9 = 24 cm.

The diagonals of a rhombus bisect each other at right angles (90°).

⇒ Side (s) = √((d₁/2)² + (d₂/2)²)

⇒ s = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.

⇒ Perimeter = 4 × s = 4 × 15 = 60 cm.

∴ The correct answer is 60 cm.

Additional Information

Diagonal Properties

The diagonals of a rhombus bisect each other at 90° and bisect the vertex angles.

Side-Diagonal Relation

The relationship between the side (s) and diagonals is given by: 4s² = d₁² + d₂².

Rhombus Area

Area of a rhombus can also be calculated as Base × Height if those values are known.

Shortcut Trick

Area of rhombus = (1/2) × d₁ × d₂

384 = (1/2) × 24 × d₂ ⇒ d₂ = 32 cm.

Half-diagonals are 12 and 16. Using Pythagorean Triplet (3, 4, 5) scaled by 4 ⇒ Side = 20 cm.

Perimeter = 4 × Side = 4 × 20 = 80 cm.

∴ The correct answer is 80 cm.

Alternate Method

Given: Area = 384 cm², Diagonal 1 (d₁) = 24 cm.

Formula Used:

1. Area = (1/2) × d₁ × d₂
2. Side (a) = √((d₁/2)² + (d₂/2)²)
3. Perimeter = 4a

Calculations:

⇒ Area = (1/2) × 24 × d₂

⇒ 384 = 12 × d₂

⇒ d₂ = 384 ÷ 12 = 32 cm

⇒ Side a = √((24/2)² + (32/2)²)

⇒ Side a = √(12² + 16²)

⇒ Side a = √(144 + 256) = √400

⇒ Side a = 20 cm

⇒ Perimeter = 4 × 20 = 80 cm

∴ The correct answer is 80 cm.

Additional Information

Properties of Rhombus

A rhombus is a quadrilateral with all sides equal. Its diagonals bisect each other at 90°.

Relation between Side and Diagonals

The side 'a' and diagonals 'd₁' and 'd₂' are related by the equation 4a² = d₁² + d₂².

Area of Rhombus

Area can also be calculated as Base × Height if the altitude is known.

Shortcut Trick

The Least Common Multiple (LCM) follows the associative property, which states that LCM(A, B, C, D) = LCM[LCM(A, B), LCM(C, D)].

⇒ Given LCM(A, B) = 20 and LCM(C, D) = 30.

⇒ Required LCM = LCM(20, 30).

⇒ The smallest number divisible by both 20 and 30 is 60.

∴ The correct answer is 60.

Alternate Method

Given:

LCM of A and B = 20

LCM of C and D = 30

Formula Used:

LCM(a, b, c, d) = LCM(LCM(a, b), LCM(c, d))

Calculations:

⇒ We need to find the LCM of 20 and 30.

⇒ Prime factorization of 20 = 2 × 2 × 5 = 2² × 5

⇒ Prime factorization of 30 = 2 × 3 × 5

⇒ LCM is the product of the highest powers of all prime factors involved.

⇒ LCM = 2² × 3 × 5

⇒ LCM = 4 × 3 × 5 = 60

∴ The correct answer is 60.

Additional Information

Associative Property of LCM

The LCM of a set of numbers can be found by grouping them: LCM(a, b, c) = LCM(a, LCM(b, c)).

Relationship between HCF and LCM

For any two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.

LCM of Fractions

LCM of (a/b, c/d) = LCM of numerators (a, c) ÷ HCF of denominators (b, d).

Shortcut Trick

The Highest Common Factor (HCF) of any set of numbers is always a factor of their Least Common Multiple (LCM).

Given LCM = 90, the potential HCF must divide 90 exactly without a remainder.

Checking options: 90 ÷ 28 (No) | 90 ÷ 24 (No) | 90 ÷ 36 (No) | 90 ÷ 15 = 6 (Yes).

Since only 15 is a factor of 90, it is the only possible HCF.

∴ The correct answer is 15.

Alternate Method

Given:

LCM of two numbers = 90

Formula/Property:

For any two integers, LCM = HCF × k (where k is a positive integer representing the product of the non-common prime factors).

Calculations:

⇒ Let the HCF be 'h'. Then 90/h must be an integer.

⇒ Option 1: 90 ÷ 28 ≈ 3.21 (Not an integer)

⇒ Option 2: 90 ÷ 24 = 3.75 (Not an integer)

⇒ Option 3: 90 ÷ 36 = 2.5 (Not an integer)

⇒ Option 4: 90 ÷ 15 = 6 (Integer)

⇒ Since 15 divides 90 perfectly, it can be the HCF.

∴ The correct answer is 15.

Additional Information

Fundamental Relation

For any two positive integers a and b: Product of numbers = HCF(a, b) × LCM(a, b).

HCF vs LCM Magnitude

The HCF is always less than or equal to the LCM. Specifically, HCF ≤ smaller number ≤ larger number ≤ LCM.

Co-prime Numbers

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

Divisibility Rule

The LCM of a set of numbers is the smallest number that is divisible by all the numbers in that set.

Shortcut Trick

To find 10% of any value, simply divide the number by 10 or shift the decimal point one place to the left.

Profit = 480 ÷ 10

Profit = Rs. 48

∴ The correct answer is Rs. 48.

Alternate Method

Given:

Cost Price (CP) of the article = Rs. 480

Profit Percentage = 10%

Formula Used:

Profit = (Profit% ÷ 100) × Cost Price

Calculations:

⇒ Profit = (10 ÷ 100) × 480

⇒ Profit = 0.1 × 480

⇒ Profit = Rs. 48

∴ The correct answer is Rs. 48.

Additional Information

Selling Price (SP) Calculation

The selling price is the sum of cost price and profit: SP = CP + Profit. In this case, SP = 480 + 48 = Rs. 528. Loss Calculation

If the article is sold for less than the CP, a loss occurs. Loss = CP − SP. Loss% = (Loss ÷ CP) × 100.

Direct SP Formula

To find SP directly when Profit% is known: SP = CP × (100 + Profit%) ÷ 100.

Shortcut Trick

When x% of x = k, the value of x is directly calculated as 10 × √k.

Here, k = 225.

⇒ x = 10 × √225

⇒ x = 10 × 15 = 150.

∴ The correct answer is 150.

Alternate Method

Given:

The expression is x percent of x is equal to 225.

Calculations:

⇒ (x ÷ 100) × x = 225

⇒ x² ÷ 100 = 225

⇒ x² = 225 × 100

⇒ x² = 22500

⇒ x = √22500

⇒ x = 150

∴ The correct answer is 150.

Additional Information

Basic Percentage Formula

The percentage of a number is calculated as: Value = (Percentage × Total) ÷ 100.

Square Root Calculation

To find the value from its square, take the square root. For example, √(a × b) = √a × √b. Here, √22500 = √225 × √100 = 15 × 10 = 150.

Percentage and Fractions

Any percentage x% can be written as a fraction x/100 or a decimal 0.01x.

Shortcut Trick

25% = 1/4 (fractional value).

Loss is calculated on Selling Price (SP), so let SP = 4 units and Loss = 1 unit.

Cost Price (CP) = SP + Loss = 4 + 1 = 5 units.

Loss percentage on Cost Price = (Loss ÷ CP) × 100 = (1 ÷ 5) × 100.

∴ The correct answer is 20%.

Alternate Method

Given:

Loss percentage on Selling Price = 25%

Formula Used:

Loss = Selling Price × (Loss% on SP ÷ 100)

Cost Price = Selling Price + Loss

Loss% on Cost Price = (Loss ÷ Cost Price) × 100

Calculations:

⇒ Let the Selling Price (SP) be ₹100.

⇒ Loss = 25% of ₹100 = (25 ÷ 100) × 100 = ₹25.

⇒ Cost Price (CP) = SP + Loss = 100 + 25 = ₹125.

⇒ Loss% on CP = (Loss ÷ CP) × 100.

⇒ Loss% = (25 ÷ 125) × 100.

⇒ Loss% = (1 ÷ 5) × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Base for Profit and Loss

Profit or loss is always calculated on the Cost Price (CP) unless the question explicitly mentions it is calculated on the selling price.

Profit Percentage Formula

Profit % = (Profit ÷ CP) × 100, where Profit = Selling Price − Cost Price.

Cost Price Conversion

If loss is x% on SP, then loss % on CP = [x ÷ (100 + x)] × 100. If profit is x% on SP, then profit % on CP = [x ÷ (100 − x)] × 100.

Shortcut Trick

Ratio of P : Q : R = 75 : 100 : 60 = 15 : 20 : 12

Total sum = 15 + 20 + 12 = 47 units

Given: 47 units = 1410 → 1 unit = 1410 ÷ 47 = 30

Difference (Q − R) = 20 − 12 = 8 units

Required difference = 8 × 30 = 240

∴ The correct answer is 240 marks.

Alternate Method

Given:

P = Q − 25% of Q

R = Q − 40% of Q

Sum of P, Q, and R = 1410

Formula Used:

Total Marks = P + Q + R

Difference = Q − R

⇒ Let the marks of Q be 100x.

⇒ Marks of P = 100x − 25% of 100x = 75x

⇒ Marks of R = 100x − 40% of 100x = 60x

⇒ Total Marks = 75x + 100x + 60x = 235x

⇒ 235x = 1410

⇒ x = 1410 ÷ 235 = 6

⇒ Difference between Q and R = 100x − 60x = 40x

⇒ Value of difference = 40 × 6 = 240

∴ The correct answer is 240 marks.

Additional Information

Percentage Base Rule

Always identify the base value (denominator) which typically follows keywords like 'than' or 'of' to set it as 100%.

Ratio Method for Percentages

Converting percentages to fractions (e.g., 25% = 1/4, 40% = 2/5) helps in establishing quick ratios between multiple entities.

Relative Percentage Change

If A is x% less than B, then the difference in their values is calculated as (x ÷ 100) × B.

Shortcut Trick

Efficiency of C = Efficiency (A + B + C) − Efficiency (A + B)

Total Work = LCM of (18, 24) = 72 units

Efficiency of (A + B + C) = 72 ÷ 18 = 4 units/day

Efficiency of (A + B) = 72 ÷ 24 = 3 units/day

Efficiency of C = 4 − 3 = 1 unit/day

∴ The correct answer is 72 days.

Alternate Method

Given:

Time taken by A, B, and C together = 18 days

Time taken by A and B together = 24 days

Formula Used:

Total Work = Time taken × Efficiency

Calculations:

⇒ Let the total work be the LCM of 18 and 24 = 72 units.

⇒ Efficiency of (A + B + C) = 72 ÷ 18 = 4 units/day.

⇒ Efficiency of (A + B) = 72 ÷ 24 = 3 units/day.

⇒ Efficiency of C = Efficiency(A + B + C) − Efficiency(A + B)

⇒ Efficiency of C = 4 − 3 = 1 unit/day.

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

⇒ Time taken by C alone = 72 ÷ 1 = 72 days.

∴ The correct answer is 72 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to the time taken to complete the work. Efficiency = 1 ÷ Time.

Combined Work Formula

If X takes 'a' days and Y takes 'b' days, then together they take (a × b) ÷ (a + b) days.

Pipes and Cisterns

The concept is identical to Time & Work, where an inlet pipe does positive work and an outlet pipe does negative work.

Work and Wages

Wages are always distributed in the ratio of the Efficiency of the workers (or work done) when they work for the same duration.

Shortcut Trick

Ratio of efficiencies (X : Y : Z) = (1/12) : (1/18) : (1/36) = 3 : 2 :

1. Since they work together, Wage ∝ Efficiency.

Given X wage = 3 units = ₹4800 ⇒ 1 unit = ₹1600.

Difference = |(Y + Z) − (X + Z)| = |Y − X| = |2 − 3| = 1 unit.

Value of 1 unit = ₹1600.

∴ The correct answer is ₹1600.

Alternate Method

Given:

Time taken by X = 12 days, Y = 18 days, Z = 36 days.

Wages of X = ₹4800.

Formula Used:

Total Work = LCM of individual days.

Efficiency = Total Work ÷ Time taken.

Wage Share = (Individual Efficiency ÷ Total Efficiency) × Total Wage.

Calculations:

⇒ Total wages are distributed in the ratio of efficiencies X : Y : Z = 3 : 2 :

1. ⇒ Wage of X = 3 units = ₹4800.

⇒ Value of 1 unit = 4800 ÷ 3 = ₹1600.

⇒ Wage of Y = 2 × 1600 = ₹3200.

⇒ Wage of Z = 1 × 1600 = ₹1600.

⇒ Total wages of (Y + Z) = 3200 + 1600 = ₹4800.

⇒ Total wages of (X + Z) = 4800 + 1600 = ₹6400.

⇒ Absolute Difference = |4800 − 6400| = ₹1600.

∴ The correct answer is ₹1600.

Additional Information

Work and Wages Rule

Wages are always distributed in the ratio of the actual work done by each person. If they work for the same duration, the wage ratio is identical to the efficiency ratio.

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. Efficiency = 1 ÷ Time.

Pipes and Cisterns

The same LCM and efficiency logic applies to pipes filling or emptying a tank, where inlet efficiency is positive and outlet efficiency is negative.

Shortcut Trick

Relative Speed in same direction = 75 − 25 = 50 km/hr.

Total Distance to cover = Sum of lengths = 120 + 130 = 250 m.

Time = Distance ÷ Relative Speed

Time = 250 ÷ (50 × 5/18) = 250 × 18 ÷ 250 = 18 sec.

∴ The correct answer is 18 sec.

Alternate Method

Given:

Length of Faster Train (L₁) = 130 m

Length of Slower Train (L₂) = 120 m

Speed of Faster Train (S₁) = 75 km/hr

Speed of Slower Train (S₂) = 25 km/hr

Formula Used:

Relative Speed (Same direction) = S₁ − S₂

Time = (L₁ + L₂) ÷ Relative Speed

Calculations:

⇒ Total Length to be crossed = 130 + 120 = 250 m

⇒ Relative Speed = 75 − 25 = 50 km/hr

⇒ Convert Speed to m/s = 50 × (5 ÷ 18) = 250 ÷ 18 m/s

⇒ Time taken = 250 ÷ (250 ÷ 18)

⇒ Time taken = 250 × (18 ÷ 250) = 18 seconds

∴ The correct answer is 18 sec.

Additional Information

Relative Speed Concept

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

Unit Conversion

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

Crossing Distance

When a train crosses another train or a bridge, the total distance covered is the sum of their lengths (L₁ + L₂).

Shortcut Trick

By definition, the Upstream speed of a boat is the difference between its speed in still water and the speed of the stream.

The question asks for this exact difference: (Speed of boat in still water − Speed of stream).

Given Upstream speed = 15 km/hr.

Required difference = 15 km/hr.

∴ The correct answer is 15 km/hr.

Alternate Method

Given:

Downstream Speed (D) = 25 km/hr

Upstream Speed (U) = 15 km/hr

Formula Used:

Speed of boat in still water (x) = (D + U) ÷ 2

Speed of stream (y) = (D − U) ÷ 2

Calculations:

⇒ Speed of boat in still water (x) = (25 + 15) ÷ 2

⇒ x = 40 ÷ 2 = 20 km/hr

⇒ Speed of stream (y) = (25 − 15) ÷ 2

⇒ y = 10 ÷ 2 = 5 km/hr

⇒ Required Difference = x − y

⇒ Required Difference = 20 − 5 = 15 km/hr

∴ The correct answer is 15 km/hr.

Additional Information

Downstream Speed

The speed of the boat when traveling with the current: Speed in Still Water + Speed of Current.

Upstream Speed

The speed of the boat when traveling against the current: Speed in Still Water − Speed of Current.

Speed of Boat Formula

Speed of boat in still water is calculated as (Downstream Speed + Upstream Speed) ÷ 2.

Speed of Current Formula

Speed of stream or current is calculated as (Downstream Speed − Upstream Speed) ÷ 2.

Shortcut Trick

Use the ratio relation: CP / MP = (100 − Discount%) / (100 + Profit%)

CP : MP = (100 − 40) : (100 + 50) = 60 : 150 = 2 : 5

Given CP = 2 units = Rs. 1000 ⇒ 1 unit = Rs. 500

Marked Price (MP) = 5 units = 5 × 500 = Rs. 2500

∴ The correct answer is Rs. 2500.

Alternate Method

Given: Cost Price (CP) = Rs. 1000, Discount = 40%, Profit = 50%.

Formula Used: SP = CP × (1 + Profit/100) and SP = MP × (1 − Discount/100).

⇒ Selling Price (SP) = 1000 + 50% of 1000

⇒ SP = 1000 + 500 = Rs. 1500

⇒ According to discount, SP = MP × (100 − 40)/100

⇒ 1500 = MP × 0.6

⇒ MP = 1500 ÷ 0.6 = Rs. 2500

∴ The correct answer is Rs. 2500.

Additional Information

Relation between MP and CP

A very useful direct relation is MP/CP = (100 + Profit%) / (100 − Discount%). This eliminates the need to calculate SP separately.

Successive Discounts

If two successive discounts of d₁% and d₂% are given, the single equivalent discount is (d₁ + d₂ − (d₁ × d₂)/100)%.

Markup Percentage

The percentage by which Marked Price is higher than Cost Price is Markup% = [(MP − CP) / CP] × 100.

Shortcut Trick

Let Cost Price (CP) = 4 units. For 25% Loss, Selling Price (SP) = 3 units.

Discount = (5/9) × SP = (5/9) × 3 = 5/3 units.

Marked Price (MP) = SP + Discount = 3 + 5/3 = 14/3 units.

Ratio of MP to CP = (14/3) ÷ 4 = 14/12 = 7/6.

∴ The correct answer is (7/6) of cost price.

Alternate Method

Given:

Loss Percentage = 25%

Discount = (5/9) × Selling Price (SP)

Formula Used:

SP = CP × (100 − Loss%)/100

MP = SP + Discount

⇒ Let Cost Price (CP) be C.

⇒ SP = C × (100 − 25)/100 = (75/100)C = (3/4)C

⇒ Marked Price (MP) = SP + Discount

⇒ MP = SP + (5/9)SP = (14/9)SP

⇒ Substituting SP = (3/4)C:

⇒ MP = (14/9) × (3/4)C

⇒ MP = (42/36)C = (7/6)C

∴ The correct answer is (7/6) of cost price.

Additional Information

Relationship between CP, MP, Profit and Discount

The formula relating CP and MP is CP/MP = (100 − Discount%)/(100 + Profit%). In case of loss, replace +Profit% with −Loss%.

Marked Price (MP)

MP is the maximum retail price (MRP) set by the seller. Discount is always calculated as a percentage of the MP: SP = MP × (100 − D%)/100.

Cost Price (CP) and Selling Price (SP)

Profit or loss is determined by the difference between SP and CP. If SP > CP, there is a Profit. If SP < CP, there is a Loss.

Shortcut Trick

Selling Price (SP) = 70% of Marked Price (MP)

⇒ SP = 0.70 × 1000 = 700

Profit = SP − Cost Price (CP)

⇒ Profit = 700 − 520 = 180

∴ The correct answer is Rs. 180.

Alternate Method

Given:

Marked Price (MP) = Rs. 1000

Discount = 30%

Cost Price (CP) = Rs. 520

Formula Used:

Selling Price (SP) = Marked Price (MP) − Discount

Profit = Selling Price (SP) − Cost Price (CP)

Calculations:

⇒ Discount Amount = (30/100) × 1000 = Rs. 300

⇒ Selling Price (SP) = 1000 − 300 = Rs. 700

⇒ Profit = 700 − 520

⇒ Profit = Rs. 180

∴ The correct answer is Rs. 180.

Additional Information

Profit Percentage

Profit % = (Profit ÷ Cost Price) × 100. It measures the gain relative to the investment.

Discount Percentage

Discount % = (Discount ÷ Marked Price) × 100. Discounts are always calculated on the Marked Price.

Relation between CP and MP

MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%). This direct ratio is useful for finding mark-up percentages.