Quantitative Aptitude PYQs

Shortcut Trick

Solve using the BODMAS rule by processing Multiplication and Division first.

27 × 2 = 54 and 44 ÷ 2 = 22.

Group positive and negative values: (91 + 54 + 16 + 22) − (38 + 31).

183 − 69 = 114.

∴ The correct answer is 114.

Alternate Method

Given:

Expression = 91 − 38 + 27 × 2 + (16) + 44 ÷ 2 − 31

Method Used:

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

Calculations:

⇒ Expression = 91 − 38 + 54 + 16 + 22 − 31

⇒ Expression = 91 + 54 + 16 + 22 − 38 − 31

⇒ Expression = 183 − 69

⇒ Expression = 114

∴ The correct answer is 114.

Additional Information

BODMAS Rule

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

Grouping Technique

In long addition/subtraction, group all positive terms together and all negative terms together to minimize errors.

Mental Math Tip

Convert complex divisions into simple fractions or multiples to speed up the Simplification process.

Shortcut Trick

The Product of two numbers = HCF × LCM.

Product = 6 × 36 = 216.

Given Sum = 30. We need factors of 216 that add up to 30.

Checking options: 12 + 18 = 30 and 12 × 18 = 216.

∴ The correct answer is 12 and 18.

Alternate Method

Let the two numbers be a and b.

Given: HCF = 6, LCM = 36, a + b = 30.

Using the property: a × b = HCF × LCM

⇒ a × b = 6 × 36 = 216

⇒ (a − b)² = (a + b)² − 4ab

⇒ (a − b)² = (30)² − 4(216)

⇒ (a − b)² = 900 − 864 = 36

⇒ a − b = √36 = 6

⇒ Adding (a + b = 30) and (a − b = 6): 2a = 36 ⇒ a = 18

⇒ Subtracting: 2b = 24 ⇒ b = 12

∴ The correct answer is 12 and 18.

Additional Information

Fundamental Property of HCF and LCM

For any two numbers 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 as a Factor

If the HCF of two numbers is h, the numbers can be represented as hx and hy, where x and y are co-prime integers (HCF of x and y is 1).

LCM in terms of HCF

Using the representation above, LCM = h × x × y. This is very useful in solving ratio-based HCF/LCM problems.

Shortcut Trick

Equalize decimal places in the numerator and denominator: √(0.1225 / 0.2500).

Simplify the fraction by removing the decimals: √(1225 / 2500).

Divide both values by 25: √(49 / 100).

Calculate the square root: 7 / 10 = 0.7.

∴ The correct answer is 0.7.

Alternate Method

Given: √(0.1225 / 0.25)

Formula: √(a / b) = √a / √b

⇒ √(0.1225 ÷ 0.25) ⇒ √(1225 × 10⁻⁴ ÷ (25 × 10⁻²)) ⇒ √((1225 ÷ 25) × 10⁻⁴⁺²) ⇒ √(49 × 10⁻²) ⇒ √0.49 ⇒ 0.7

∴ The correct answer is 0.7.

Additional Information

Square Root of Decimals

When finding the square root of a decimal, the number of digits after the decimal point in the result is exactly half of that in the original number (e.g., √0.0001 = 0.01).

Squares Ending in 25

Any number ending in 5, when squared, results in a number ending in 25. For example, (35)² = (3 × 4) followed by 25 = 1225.

Fraction Simplification

Always try to simplify radicands by finding common factors or converting decimals to powers of 10 before applying the square root operation.

Shortcut Trick

Identify the expression in the form [(a + b)² + (a − b)²] / (a² + b²).

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

The expression simplifies to 2(a² + b²) / (a² + b²) = 2.

Since the result is a constant, the specific values 4.2 and 3.8 do not change the final answer.

∴ The correct answer is 2.

Alternate Method

Given:

Expression = ((4.2 + 3.8)² + (4.2 − 3.8)²) / (4.2 × 4.2 + 3.8 × 3.8)

Formula Used:

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

Calculations:

⇒ Let a = 4.2 and b = 3.8.

⇒ Numerator = (4.2 + 3.8)² + (4.2 − 3.8)²

⇒ Numerator = (8.0)² + (0.4)²

⇒ Numerator = 64 + 0.16 = 64.16

⇒ Denominator = (4.2 × 4.2) + (3.8 × 3.8)

⇒ Denominator = 17.64 + 14.44 = 32.08

⇒ Final Value = 64.16 ÷ 32.08

⇒ Final Value = 2

∴ The correct answer is 2.

Additional Information

Difference of Squares of Sum and Difference

The identity (a + b)² − (a − b)² = 4ab is frequently used in simplification and algebra problems.

Standard Expansion Identities

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are the foundation for more complex quadratic reductions.

Sum of Squares

a² + b² can be expressed as [(a + b)² + (a − b)²] ÷ 2, which is the direct derivation for the given question.

Shortcut Trick

Solve for square roots first: √81 = 9, √9 = 3, and √36 = 6.

Evaluate x using BODMAS: 9 ÷ 3 + 6 = 3 + 6 = 9.

The required value is 2x = 2 × 9 = 18.

∴ The correct answer is 18.

Alternate Method

Given: x = √81 ÷ √9 + √36

Formula Used: Order of operations (BODMAS) where Division is performed before Addition.

⇒ x = 9 ÷ 3 + 6

⇒ x = 3 + 6

⇒ x = 9

To find the value of 2x:

⇒ 2x = 2 × 9

⇒ 2x = 18

∴ The correct answer is 18.

Additional Information

BODMAS Rule

This rule specifies the precedence of operations: Brackets, Orders (powers/roots), Division and Multiplication, followed by Addition and Subtraction.

Square Roots of Perfect Squares

Knowing perfect squares helps in quick simplification (e.g., 6² = 36, 9² = 81).

Linear Expressions

When a variable x is solved, any expression like nx is calculated by multiplying the constant n with the found value of x.

Shortcut Trick

Identify prime numbers between 40 and 50 directly.

The numbers are 41, 43, and 47.

Sum = 41 + 43 + 47 = 131.

∴ The correct answer is 131.

Alternate Method

Given: Range of numbers from 40 to 50.

Step 1: List all integers between 40 and 50.

⇒ Integers: 41, 42, 43, 44, 45, 46, 47, 48, 49.

Step 2: Test each number for primality (divisibility by 2, 3, 5, 7, etc.).

⇒ 41: Not divisible by 2, 3, 5, or 7. (Prime)

⇒ 42: Even number. (Composite)

⇒ 43: Not divisible by 2, 3, 5, or 7. (Prime)

⇒ 44: Even number. (Composite)

⇒ 45: Divisible by 5. (Composite)

⇒ 46: Even number. (Composite)

⇒ 47: Not divisible by 2, 3, 5, or 7. (Prime)

⇒ 48: Even number. (Composite)

⇒ 49: Divisible by 7 (7 × 7). (Composite)

Step 3: Calculate the sum of the identified primes.

⇒ Sum = 41 + 43 + 47

⇒ Sum = 131

∴ The correct answer is 131.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself. The smallest prime number is 2 (the only even prime).

Composite Numbers

A composite number has more than two factors. For example, 49 is composite because its factors are 1, 7, and 49.

Primes up to 100

There are 25 prime numbers between 1 and 100. Identifying them often involves checking divisibility by primes up to √n.

Shortcut Trick

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

Here, a = 1 and b = √5

⇒ (1 + √5)² − (1 − √5)² = 4 × 1 × √5 = 4√5

⇒ 4√5 − 14√5 = −10√5

∴ The correct answer is −10√5.

Alternate Method

Given: (1 + √5)² − (1 − √5)² − 14√5

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

⇒ [(1)² + (√5)² + 2 × 1 × √5] − [(1)² + (√5)² − 2 × 1 × √5] − 14√5

⇒ [1 + 5 + 2√5] − [1 + 5 − 2√5] − 14√5

⇒ (6 + 2√5) − (6 − 2√5) − 14√5

⇒ 6 + 2√5 − 6 + 2√5 − 14√5

⇒ 4√5 − 14√5

⇒ −10√5

∴ The correct answer is −10√5.

Additional Information

Algebraic Identities

The identity (a + b)² − (a − b)² = 4ab is used to quickly find the difference between the squares of conjugate sums.

Sum of Conjugate Squares

Another useful related identity is (a + b)² + (a − b)² = 2(a² + b²).

Square of a Binomial

The base expansion for any binomial is (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

To find the sum of n natural numbers from 1 to 35, use the direct formula: [n × (n + 1)] ÷ 2.

Here, n = 35.

Required Sum = (35 × 36) ÷ 2 = 35 × 18 = 630.

∴ The correct answer is 630.

Alternate Method

Given:

The series is an Arithmetic Progression (AP): 1, 2, 3, ..., 35.

Formula Used:

Sum of an AP, S_n = (n ÷ 2) × (a + l), where a is the first term, l is the last term, and n is the total number of terms.

Calculations:

⇒ First term (a) = 1

⇒ Last term (l) = 35

⇒ Total terms (n) = 35

⇒ S₃₅ = (35 ÷ 2) × (1 + 35)

⇒ S₃₅ = 17.5 × 36

⇒ S₃₅ = 630

∴ The correct answer is 630.

Additional Information

Sum of first n odd numbers

The sum of the first n odd natural numbers (1 + 3 + 5 + ... + (2n − 1)) is equal to n².

Sum of first n even numbers

The sum of the first n even natural numbers (2 + 4 + 6 + ... + 2n) is equal to n × (n + 1).

Sum of squares of first n natural numbers

The sum of squares (1² + 2² + ... + n²) is given by the formula [n × (n + 1) × (2n + 1)] ÷ 6.

Shortcut Trick

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

The last three digits of 73P2 are 3P2.

Checking the options: 302 ÷ 8 = 37.75 (No), 312 ÷ 8 = 39 (Yes), 352 ÷ 8 = 44 (Yes), 392 ÷ 8 = 49 (Yes).

Only P = 0 does not satisfy the condition.

∴ The correct answer is 0.

Alternate Method

Given: The number is 73P2 and it is divisible by 8.

Formula Used: Divisibility rule of 8 → The last 3 digits of a number must be divisible by 8.

⇒ The last three digits are 3P2.

⇒ For P = 0, last three digits = 302. 302 ÷ 8 = 37.75 (Remainder = 6, not divisible).

⇒ For P = 1, last three digits = 312. 312 ÷ 8 = 39 (Remainder = 0, divisible).

⇒ For P = 5, last three digits = 352. 352 ÷ 8 = 44 (Remainder = 0, divisible).

⇒ For P = 9, last three digits = 392. 392 ÷ 8 = 49 (Remainder = 0, divisible).

⇒ Since 302 is the only value not divisible by 8, P cannot be 0.

∴ The correct answer is 0.

Additional Information

Divisibility Rule of 4

A number is divisible by 4 if its last two digits are divisible by 4.

Divisibility Rule of 16

A number is divisible by 16 if its last four digits are divisible by 16.

General 2ⁿ Rule

A number is divisible by 2ⁿ if its last n digits are divisible by 2ⁿ.

Shortcut Trick

Identify the Pythagorean triplet with a hypotenuse of 17: (8, 15, 17).

Check if these dimensions satisfy the Area condition: 15 × 8 = 120 cm² (Correct).

Calculate the Perimeter = 2 × (Length + Breadth).

⇒ 2 × (15 + 8) = 2 × 23 = 46 cm.

∴ The correct answer is 46 cm.

Alternate Method

Given: Area (L × W) = 120 cm², Diagonal (d) = 17 cm.

Formula Used: L² + W² = d² and (L + W)² = L² + W² + 2LW.

⇒ L² + W² = 17² = 289

⇒ 2 × (L × W) = 2 × 120 = 240

⇒ (L + W)² = (L² + W²) + 2LW

⇒ (L + W)² = 289 + 240 = 529

⇒ L + W = √529 = 23 cm

⇒ Perimeter = 2(L + W) = 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 triplets include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Perimeter and Area Relationship

For a rectangle, the square of the sum of sides relates to the diagonal and area by the equation: (Sum of sides)² = Diagonal² + 2 × Area.

Rectangle Properties

A rectangle is a quadrilateral with four right angles. Its diagonals are equal in length and bisect each other.

Shortcut Trick

The difference between the averages of two pairs with a common element (m) is always half the difference between the distinct elements (l and n).

Shortcut formula: |l − n| = 2 × |Difference in averages|

⇒ |l − n| = 2 × 23

⇒ |l − n| = 46

∴ The correct answer is 46.

Alternate Method

Given:

Average of l and m = (l + m) ÷ 2

Average of m and n = (m + n) ÷ 2

Difference between these averages = 23

Calculations:

⇒ [(l + m) ÷ 2] − [(m + n) ÷ 2] = 23

⇒ (l + m − m − n) ÷ 2 = 23

⇒ (l − n) ÷ 2 = 23

⇒ l − n = 23 × 2

⇒ l − n = 46

∴ The correct answer is 46.

Additional Information

Average of Grouped Terms

The average of a set of n numbers is the sum of all numbers divided by n. Sum = Average × n.

Effect of Constant Difference

If the difference between the sums of two groups is d, and both groups have the same number of elements k, the difference between their averages is d ÷ k.

Arithmetic Progression Average

For any Arithmetic Progression (AP), the average is exactly equal to the middle term (if n is odd) or the mean of the two middle terms (if n is even).

Shortcut Trick

Profit % = 20% = 1/5 (where 5 is CP and 1 is Profit)

Selling Price (SP) = CP + Profit = 5 + 1 = 6 units

Given: 6 units = ₹2400 ⇒ 1 unit = ₹400

Cost Price (CP) = 5 units = 5 × ₹400 = ₹2000

∴ The correct answer is ₹2000.

Alternate Method

Given:

Selling Price (SP) of the article = ₹2400

Profit Percentage = 20%

Formula Used:

Cost Price (CP) = [SP × 100] ÷ [100 + Profit %]

Calculations:

⇒ CP = [2400 × 100] ÷ [100 + 20]

⇒ CP = 240000 ÷ 120

⇒ CP = 2000

∴ The correct answer is ₹2000.

Additional Information

Profit and Loss Basics

Profit = SP − CP, when SP > CP. Loss = CP − SP, when CP > SP.

Loss Percentage Formula

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

Marked Price and Discount

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

Shortcut Trick

Identify the ratio of B to A as 9X : 4X = 9 : 4.

Apply the fraction-to-percentage conversion: 9/4 × 100.

Since 1/4 is 25%, 9 × 25% = 225%.

∴ The correct answer is 225%.

Alternate Method

Given: A = 4X and B = 9X.

Formula Used: Percentage = (Value ÷ Base) × 100

⇒ Required Percentage = (B ÷ A) × 100

⇒ Percentage = (9X ÷ 4X) × 100

⇒ Percentage = (9 ÷ 4) × 100

⇒ Percentage = 2.25 × 100

⇒ Percentage = 225%

∴ The correct answer is 225%.

Additional Information

Base Identification

In the phrase 'B is what percent of A', the quantity following 'of' (which is A) is always the base (denominator).

Percentage vs. Percentage More

If B is 225% of A, then B is 125% more than A. Percentage More = ((B−A)/A) × 100.

Reciprocal Percentage

To find A as a percent of B: (4/9) × 100 ≈ 44.44%.

Shortcut Trick

Convert all units to cm: True Height = 470 cm and Estimated Height = 352 cm.

Error = 470 − 352 = 118 cm.

Error % = (Error / Original Value) × 100 = (118 / 470) × 100.

Approximation: 118 / 470 ≈ 1/4 = 25% (Exact calculation: 25.106...%).

∴ The correct answer is 25.11%.

Alternate Method

Given:

True Height = 4 m 70 cm = (4 × 100) + 70 = 470 cm

Estimated Height = 3 m 52 cm = (3 × 100) + 52 = 352 cm

Formula:

Error Percentage = (Absolute Error / True Value) × 100

Calculations:

⇒ Absolute Error = True Value − Estimated Value

⇒ Absolute Error = 470 − 352 = 118 cm

⇒ Error % = (118 / 470) × 100

⇒ Error % = 1180 / 47

⇒ Error % ≈ 25.10638...

⇒ Error % ≈ 25.11%

∴ The correct answer is 25.11%.

Additional Information

Absolute Error

It is the numerical difference between the measured value and the true value, expressed as |True Value − Measured Value|.

Relative Error

It is the ratio of the absolute error to the true value of the quantity being measured: Relative Error = Absolute Error / True Value.

Unit Conversion

Always ensure all measurements are in the same unit before calculation (1 meter = 100 cm).

Percentage Change

The formula for percentage increase or decrease is (Difference / Original Value) × 100.

Shortcut Trick

Ratio of Cost Price (CP) to Selling Price (SP) is the inverse of their percentage coefficients.

CP : SP = 30 : 40 = 3 : 4

Profit = 4 − 3 = 1 unit

Profit % = (1 / 3) × 100 = 33.33%

∴ The correct answer is 33.33%.

Alternate Method

Given:

40% of Cost Price (CP) = 30% of Selling Price (SP)

Formula Used:

Profit % = [(SP − CP) / CP] × 100

⇒ (40 / 100) × CP = (30 / 100) × SP

⇒ 40 × CP = 30 × SP

⇒ CP / SP = 30 / 40

⇒ CP / SP = 3 / 4

⇒ Let CP = 3 units and SP = 4 units.

⇒ Profit = SP − CP = 4 − 3 = 1 unit

⇒ Profit Percentage = (1 / 3) × 100

⇒ Profit % = 33.33%

∴ The correct answer is 33.33%.

Additional Information

Profit and Loss Base

Profit % and Loss % are always calculated on the Cost Price (CP) unless the question specifically mentions the Selling Price.

Relationship between CP and SP

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

Remaining food is sufficient for 1000 men for 50 days (60 − 10).

New strength = 1000 − 500 = 500 men.

Apply M₁D₁ = M₂D₂ logic on the remaining food.

1000 × 50 = 500 × D₂ ⇒ D₂ = 100 days.

∴ The correct answer is 100 days.

Alternate Method

Given:

Initial men (M₁) = 1000

Initial days = 60

Time passed = 10 days

Men left = 500

Total initial food units = 1000 × 60 = 60,000 units

Food consumed in 10 days = 1000 × 10 = 10,000 units

⇒ Remaining food = 60,000 − 10,000 = 50,000 units

⇒ Remaining men = 1000 − 500 = 500 men

⇒ Number of days = Remaining food ÷ Remaining men

⇒ Days = 50,000 ÷ 500

⇒ Days = 100 days

∴ The correct answer is 100 days.

Additional Information

Chain Rule Formula

For work and time problems, the relation is M₁D₁H₁/W₁ = M₂D₂H₂/W₂, where M is men, D is days, H is hours, and W is work.

Inverse Proportion

When the amount of food (work) is constant, the number of men is inversely proportional to the number of days (M ∝ 1/D).

Food Provision Logic

Always calculate the remaining resource first and then divide by the new capacity to find the extended duration.

Shortcut Trick

Ratio of Efficiency (and Wages) of X : Y : Z = 1/10 : 1/15 : 1/30.

Multiply by LCM (30) ⇒ 3 : 2 :

1. Given X share (3 units) = ₹8000.

Combined share of Y and Z = 2 + 1 = 3 units.

Since 3 units = ₹8000, then Y + Z share is also ₹8000.

∴ The correct answer is ₹8000.

Alternate Method

Given: Days taken by X = 10, Y = 15, Z = 30. Wage of X = ₹8000.

Formula Used: Efficiency = Total Work ÷ Time. Wages are distributed in the ratio of efficiency when time is constant.

⇒ Ratio of efficiency X : Y : Z = 3 : 2 : 1

⇒ Let efficiency (wage share) be 3k, 2k, and 1k.

⇒ 3k = ₹8000

⇒ Wage of Y and Z = 2k + 1k = 3k

⇒ Total wage of Y and Z = ₹8000

∴ The correct answer is ₹8000.

Additional Information

Wage Distribution Rule

When workers work for the same duration, wages are proportional to their efficiency. If time varies, Wage ∝ Efficiency × Time.

Inverse Relation of Time and Efficiency

Efficiency is inversely proportional to the time taken to complete the work (E = 1/T).

Combined Work Formula

If X and Y do work in 'a' and 'b' days, together they take (a × b) ÷ (a + b) days.

Shortcut Trick

When Distance is constant, Speed is inversely proportional to Time (S ∝ 1/T).

Ratio of Speeds of A and B = 14 : 38 = 7 : 19.

Ratio of Time taken (A : B) = Inverse of Speed Ratio = 19 : 7.

∴ The correct answer is 19 : 7.

Alternate Method

Given:

Speed of A (S_A) = 14 km/hr

Speed of B (S_B) = 38 km/hr

Formula Used:

Time = Distance ÷ Speed

Calculations:

Let the common distance be D km.

⇒ Time taken by A (T_A) = D ÷ 14

⇒ Time taken by B (T_B) = D ÷ 38

⇒ Required Ratio = T_A : T_B

⇒ Required Ratio = (D/14) : (D/38)

⇒ Required Ratio = 38 : 14

⇒ Required Ratio = (38 ÷ 2) : (14 ÷ 2) = 19 : 7

∴ The correct answer is 19 : 7.

Additional Information

Inverse Relationship of Speed and Time

For a fixed distance, if the speed ratio is x : y, then the time ratio will be y :

x. Average Speed Formula

When a person covers equal distances at speeds x and y, the average speed is given by [2 × x × y] ÷ [x + y].

Relative Speed

Relative speed is S₁ − S₂ for objects moving in the same direction and S₁ + S₂ for objects moving in opposite directions.

Shortcut Trick

Relative Speed when moving in opposite directions = Total Distance ÷ Time

Relative Speed = 500 ÷ 5 = 100 km/hr

Speed of H = Relative Speed − Speed of G

Speed of H = 100 − 60 = 40 km/hr

∴ The correct answer is 40 km/hr.

Alternate Method

Given:

Total distance between P and Q = 500 km

Meeting time = 5 hours

Speed of G = 60 km/hr

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Distance covered by G in 5 hours = Speed × Time

⇒ Distance (G) = 60 × 5 = 300 km

⇒ Since they meet at S, the remaining distance is covered by H.

⇒ Distance covered by H = Total Distance − Distance (G)

⇒ Distance (H) = 500 − 300 = 200 km

⇒ Speed of H = Distance (H) ÷ Time

⇒ Speed of H = 200 ÷ 5 = 40 km/hr

∴ The correct answer is 40 km/hr.

Additional Information

Relative Speed in Opposite Direction

When two objects move towards each other, their relative speed is the sum of their individual speeds: V_rel = S₁ + S₂.

Relative Speed in Same Direction

When two objects move in the same direction, their relative speed is the difference between their individual speeds: V_rel = |S₁ − S₂|.

Meeting Point Logic

If two objects start at the same time and meet, the time taken by both to reach the meeting point is identical.

Shortcut Trick

Let the Marked Price (X) be 100 units.

Purchase Price (Y) = 100 − 40% = 60 units.

Selling Price (Z) = 60 + 30% of 60 = 60 + 18 = 78 units.

Required Ratio Z : X = 78 : 100 = 39 : 50.

∴ The correct answer is 39 : 50.

Alternate Method

Given:

Marked Price = X

Discount = 40% on X

Purchase Price (Y) = X − (40/100) × X = 0.6X

Selling Price (Z) = Y + 30% of Y = 1.3Y

Calculations:

⇒ Y = 0.6X

⇒ Z = 1.3 × (0.6X)

⇒ Z = 0.78X

⇒ Z / X = 0.78

⇒ Z / X = 78 / 100

⇒ Z / X = 39 / 50

⇒ Z : X = 39 : 50

∴ The correct answer is 39 : 50.

Additional Information

Marked Price and Discount

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

Profit Percentage

Selling Price = Cost Price × (100 + Profit%) ÷ 100. Profit is generally calculated on the Cost Price (or Purchase Price).

Successive Percentage Change

When a value is changed by a% and then by b%, the net change is [a + b + (a × b)/100]%. For discounts, use negative values.