Quantitative Aptitude PYQs

Shortcut Trick

Assume all 200 tickets sold were Youth tickets: Total = 200 × ₹150 = ₹30,000.

Extra revenue earned = Actual revenue − Assumed revenue = ₹38,000 − ₹30,000 = ₹8,000.

Difference between Adult and Youth ticket price = ₹250 − ₹150 = ₹100.

Number of Adult tickets = 8,000 ÷ 100 = 80 tickets.

Number of Youth tickets = Total − Adult = 200 − 80 = 120 tickets.

∴ The correct answer is 120 youth tickets and 80 adult tickets.

Alternate Method

Given: Youth ticket price = ₹150, Adult ticket price = ₹250, Total tickets = 200, Total Revenue = ₹38,000.

Method: We can use the Alligation Method by finding the Average Price per ticket.

⇒ Average price per ticket = Total Revenue ÷ Total Tickets

⇒ Average price = 38,000 ÷ 200 = ₹190.

⇒ Ratio of Youth tickets : Adult tickets = 60 : 40 = 3 : 2.

⇒ Total ratio parts = 3 + 2 = 5 units.

⇒ 5 units = 200 tickets.

⇒ 1 unit = 200 ÷ 5 = 40 tickets.

⇒ Youth tickets = 3 units = 3 × 40 = 120 tickets.

⇒ Adult tickets = 2 units = 2 × 40 = 80 tickets.

∴ The correct answer is 120 youth tickets and 80 adult tickets.

Additional Information

Linear Equations Method

This problem can also be solved using simultaneous equations: x + y = Total Quantity and (Price₁ × x) + (Price₂ × y) = Total Value.

Alligation Rule

Quantity of Cheaper / Quantity of Dearer = (Price of Dearer − Mean Price) / (Mean Price − Price of Cheaper).

Weighted Average

The overall average price of a mixture depends on the individual prices and the quantity (weight) of each component: A_avg = (n₁v₁ + n₂v₂) ÷ (n₁ + n₂).

Shortcut Trick
For the equation X/75 = 12/X, the value of X is the geometric mean of the two denominators/numerators.
X2 = 75 × 12
X = √(75 × 12) = √(900) = 30
∴ The correct answer is 30.
Alternate Method
Given:
Equation: X/75 = 12/X where X > 0
Formula Used:
Cross-multiplication: a/b = c/d ⇒ a × d = b × c
Calculations:
⇒ X/75 = 12/X
⇒ X × X = 75 × 12
⇒ X2 = 900
⇒ X = √900
⇒ X = 30 (Since X > 0)
∴ The correct answer is 30.
Additional Information
Mean Proportional
If a/x = x/b, then x is called the mean proportional between a and b, calculated as x = √(ab).
Quadratic Roots
A quadratic equation of the form x2 = k has two roots, √k and −√k. The condition X > 0 filters the positive root.

Shortcut Trick

Find factors of xy = 18 whose difference (x − y) is 3.

Possible pairs for 18 are (18, 1), (9, 2), and (6, 3).

Since 6 − 3 = 3, we have x = 6 and y = 3.

Substitute these in x² − y²: 6² − 3² = 36 − 9 = 27.

∴ The correct answer is 27.

Alternate Method

Given:

x − y = 3

xy = 18

Formula Used:

(x + y)² = (x − y)² + 4xy

x² − y² = (x − y)(x + y)

Calculations:

⇒ (x + y)² = 3² + 4 × 18

⇒ (x + y)² = 9 + 72

⇒ (x + y)² = 81

⇒ x + y = √81 = 9

Now, calculate x² − y²:

⇒ x² − y² = (x − y)(x + y)

⇒ x² − y² = 3 × 9

⇒ x² − y² = 27

∴ The correct answer is 27.

Additional Information

Difference of Squares

The algebraic identity for the difference of two squares is given by a² − b² = (a − b)(a + b).

Relationship between Sum and Difference

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

Square of a Binomial

Standard identities: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

Identify the total number of days: Feb (24) + Mar (31) + Apr (18) = 73 days.

In competitive exams, 73 days is a standard value equal to exactly 1/5 of a year (73 ÷ 365 = 1/5).

Simple Interest = (Principal × Rate × Time) ÷ 100

Simple Interest = (2000 × 7 × 1/5) ÷ 100 = 400 × 7 ÷ 100 = ₹28.

∴ The correct answer is ₹28.

Alternate Method

Given:

Principal (P) = ₹2,000

Rate of Interest (R) = 7% per annum

Time Period = 4 February 2023 to 18 April 2023

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ Number of days in February (non-leap year) = 28 − 4 = 24 days

⇒ Number of days in March = 31 days

⇒ Number of days in April = 18 days

⇒ Total Days = 24 + 31 + 18 = 73 days

⇒ Time (T) in years = 73 ÷ 365 = 1/5 years

⇒ SI = (2000 × 7 × 1/5) ÷ 100

⇒ SI = (400 × 7) ÷ 100

⇒ SI = 2800 ÷ 100 = 28

∴ The correct answer is ₹28.

Additional Information

Day Counting Rule

While calculating the number of days between two dates, usually the starting day is excluded and the last day is included.

Leap Year Consideration

Always check the year; if it is divisible by 4 (e.g., 2024), February has 29 days. Since 2023 is not divisible by 4, we used 28 days.

Standard Conversions

In interest problems, 73 days = 1/5 year and 146 days = 2/5 year are very common values used to simplify calculations.

Shortcut Trick

Combined efficiency of Arun + Manish + Tarun = (Total Work ÷ Days) / 2 = (4 + 5 + 6) ÷ 2 = 7.5 units/day.

Efficiency of Arun = Combined efficiency (A+M+T) − Efficiency of (M+T) = 7.5 − 5 = 2.5 units/day.

Time taken by Arun alone = Total Work ÷ Efficiency = 60 ÷ 2.5 = 24 days.

∴ The correct answer is 24 days.

Alternate Method

Given:

Arun and Manish (A + M) = 15 days

Manish and Tarun (M + T) = 12 days

Tarun and Arun (T + A) = 10 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Time

Calculations:

⇒ 2 × (Arun + Manish + Tarun) = 4 + 5 + 6 = 15

⇒ Arun + Manish + Tarun = 15 ÷ 2 = 7.5

⇒ Arun's efficiency = (Arun + Manish + Tarun) − (Manish + Tarun)

⇒ Arun's efficiency = 7.5 − 5 = 2.5

⇒ Days taken by Arun = 60 ÷ 2.5

⇒ Days taken by Arun = 24

∴ The correct answer is 24 days.

Additional Information

Total Combined Efficiency

When pairs are given like (A+B), (B+C), and (C+A), the sum of their efficiencies is twice the efficiency of (A+B+C).

Work & Wages

Wages are always distributed in the ratio of the work done or the ratio of efficiencies when time taken is same.

Alternate Day Work

For alternate days, calculate work done in one cycle (sum of efficiencies) and then divide total work by cycle work.

Shortcut Trick

Distance from bottom (base) = 15 units.

Distance from top (hypotenuse) = 2 × 15 = 30 units.

Using the property of a 30-60-90 triangle where hypotenuse is double the base.

Height = Base × √3 = 15√3 units.

∴ The correct answer is 15√3 units.

Alternate Method

Given: Distance from bottom (BC) = 15 units. Distance from top (AC) = 2 × BC = 30 units.

Formula Used: Pythagoras Theorem: AB² + BC² = AC²

⇒ Let AB be the height of the building (h).

⇒ h² + 15² = 30²

⇒ h² + 225 = 900

⇒ h² = 900 − 225

⇒ h² = 675

⇒ h = √675 = √(225 × 3)

⇒ h = 15√3 units.

∴ The correct answer is 15√3 units.

Additional Information

Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

30-60-90 Triangle Ratio

The sides of a 30-60-90 triangle are always in the ratio 1 : √3 : 2. If the shortest side (opposite 30°) is x, the hypotenuse is 2x and the height is x√3.

Trigonometric Ratios

cos θ = Base / Hypotenuse. In this case, cos θ = 15/30 = 1/2, which means the angle of elevation θ is 60°.

Shortcut Trick

Assume a base value (Assumed Mean) near the middle, say 50.

Calculate deviations from 50: −8, −21, −8, +8, −32, −11, −9, +29, +43.

Net deviation = −8 − 21 − 8 + 8 − 32 − 11 − 9 + 29 + 43 = −9.

Average deviation = −9 ÷ 9 = −1.

Actual Mean = Assumed Mean + Average Deviation = 50 + (−1) = 49.

∴ The correct answer is 49.

Alternate Method

Given Observations: 42, 29, 42, 58, 18, 39, 41, 79, 93

Total count (n): 9

Formula Used: Arithmetic Mean = (Sum of all observations) ÷ (Number of observations)

⇒ Sum = 42 + 29 + 42 + 58 + 18 + 39 + 41 + 79 + 93

⇒ Sum = 441

⇒ Arithmetic Mean = 441 ÷ 9

⇒ Arithmetic Mean = 49

∴ The correct answer is 49.

Additional Information

Properties of Arithmetic Mean

The sum of deviations of items from their arithmetic mean is always zero (∑(x − x̄) = 0).

Effect of Changes

If each observation is increased, decreased, multiplied, or divided by a constant k, the mean also changes by that same constant k.

Combined Mean

If two groups have means x̄₁ and x̄₂ with sizes n₁ and n₂, the combined mean is (n₁x̄₁ + n₂x̄₂) ÷ (n₁ + n₂).

Shortcut Trick

Sum of reciprocals of two numbers = (Sum of numbers) ÷ (Product of numbers)

We know that Product of numbers = HCF × LCM

Sum of reciprocals = 60 ÷ (12 × 72)

Sum of reciprocals = 5 ÷ 72

∴ The correct answer is 5/72.

Alternate Method

Given:

Sum of two numbers (x + y) = 60

HCF = 12, LCM = 72

Formula Used:

Product of two numbers (x × y) = HCF × LCM

Sum of reciprocals = (1/x) + (1/y) = (x + y) / (xy)

Calculations:

⇒ Product (xy) = 12 × 72 = 864

⇒ Sum of reciprocals = 60 / 864

⇒ Dividing both numerator and denominator by 12:

⇒ 60 / 864 = 5 / 72

∴ The correct answer is 5/72.

Additional Information

HCF and LCM Relation

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

Reciprocal Sum Property

The sum of the reciprocals of any two numbers is always equal to the sum of the numbers divided by their product.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is equal to their product.

Shortcut Trick

Total Surface Area (TSA) = Total Cost ÷ Rate = 100602 ÷ 23 = 4374 cm²

Side of the cube (a) = √(TSA ÷ 6) = √(4374 ÷ 6) = √729 = 27 cm

Volume of the cube = a³ = 27³ = 19,683 cm³

∴ The correct answer is 19,683 cm³.

Alternate Method

Given:

Total cost of painting = ₹1,006.02

Rate of painting = 23 paise per cm²

Formula Used:

Total Surface Area (TSA) of a cube = 6 × a²

Volume of a cube = a³ (where 'a' is the side of the cube)

Calculations:

⇒ Total Cost in paise = 1006.02 × 100 = 100,602 paise

⇒ Total Surface Area (TSA) = Total Cost ÷ Rate = 100,602 ÷ 23

⇒ TSA = 4,374 cm²

⇒ 6 × a² = 4,374

⇒ a² = 4,374 ÷ 6 = 729

⇒ a = √729 = 27 cm

⇒ Volume = a³ = 27 × 27 × 27

⇒ Volume = 19,683 cm³

∴ The correct answer is 19,683 cm³.

Additional Information

Lateral Surface Area (LSA)

The surface area of the four vertical faces of a cube is given by 4a².

Diagonal of a Cube

The length of the longest rod that can be placed inside a cube is its diagonal, calculated as d = a√3.

Unit Conversion

Always ensure the units of cost and rate are the same (either both in Rupees or both in Paise) before calculation.

Shortcut Trick

In right-angled ΔBDC, ∠C = 90° − ∠DBC = 90° − 33° = 57°.

In ΔAEC, ∠AEB is the exterior angle at vertex E.

By the Exterior Angle Theorem, ∠AEB = ∠CAE + ∠ACE.

⇒ ∠AEB = 70° + 57° = 127°.

∴ The correct answer is 127°.

Alternate Method

Given: BD ⊥ AC, ∠DBC = 33°, ∠CAE = 70°.

In ΔBDC, ∠BDC = 90° (since BD ⊥ AC).

⇒ ∠BCD = 180° − (∠BDC + ∠DBC)

⇒ ∠BCD = 180° − (90° + 33°) = 57°.

Shortcut Trick

The Marked Price (MP) is always considered as 100%.

If Discount = 54%, then Selling Price (SP) = 100% − 54% = 46%.

According to the question, 46% → ₹ 29,946.

1% → 29,946 ÷ 46 = ₹ 651.

100% (MP) → 651 × 100 = ₹ 65,100.

∴ The correct answer is ₹ 65,100.

Alternate Method

Given: Selling Price (SP) = ₹ 29,946 and Discount% = 54%.

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

⇒ 29,946 = MP × (100 − 54) ÷ 100

⇒ 29,946 = MP × 46 ÷ 100

⇒ MP = (29,946 × 100) ÷ 46

⇒ MP = 651 × 100

⇒ MP = ₹ 65,100.

∴ The correct answer is ₹ 65,100.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on an item. Discount is always calculated on the Marked Price. Formula: SP = MP − Discount.

Discount Percentage

It is the ratio of discount to the marked price expressed as a percentage. Formula: Discount% = (Discount ÷ MP) × 100.

Shortcut Trick

Ratio of Teacher to Student age: Current = 4 : 1, Five years ago = 7 :

1. Make the ratio difference equal: (4:1)×6 → 24:6 and (7:1)×3 → 21:3.

Difference in ratio units = 24 − 21 = 3 units, which corresponds to 5 years.

Current age of Teacher = 24 units → (5/3) × 24 = 40 years.

∴ The correct answer is 40 years.

Alternate Method

Given:

Let the current age of the Student be x.

Current age of the Teacher = 4x.

Calculations:

⇒ Age of Student 5 years ago = x − 5

⇒ Age of Teacher 5 years ago = 4x − 5

⇒ According to the problem: 4x − 5 = 7 × (x − 5)

⇒ 4x − 5 = 7x − 35

⇒ 3x = 30

⇒ x = 10

⇒ Current age of Teacher = 4 × 10 = 40 years.

∴ The correct answer is 40 years.

Additional Information

Age Ratio Constant Difference

The numerical difference between the ages of two persons remains constant regardless of how many years pass.

Linear Equation Method

For age problems, always define the variable based on the current age to simplify calculations for past or future conditions.

Shortcut Trick

Combined efficiency (P+Q) = 60 ÷ 12 = 5 units/hr (Let Total Work = 60 units)

Efficiency of P = 60 ÷ 30 = 2 units/hr

Efficiency of Q = 5 − 2 = 3 units/hr

Time for Q to fill 1/4 of tank = (60 ÷ 4) ÷ 3 = 15 ÷ 3 = 5 hours

∴ The correct answer is 5 hours.

Alternate Method

Given:

Time taken by P and Q together = 12 hours

Time taken by P alone = 30 hours

Calculations:

⇒ Efficiency of Q = Efficiency of (P + Q) − Efficiency of P

⇒ Efficiency of Q = 5 − 2 = 3 units/hr

⇒ One-fourth of total tank capacity = 60 ÷ 4 = 15 units

⇒ Time taken by Q = Work ÷ Efficiency

⇒ Time = 15 ÷ 3 = 5 hours

∴ The correct answer is 5 hours.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to time. If a person takes 'n' days to complete a work, efficiency = 1/n units per day.

Pipes and Cisterns

Inlet pipes have positive efficiency, while outlet (leakage) pipes have negative efficiency. Net work = Sum of efficiencies.

Shortcut Trick

Combine ratios A : B = 3 : 1 and B : C = 7 : 12 to get A : B : C = 21 : 7 : 12.

Total units = 21 + 7 + 12 = 40 units.

Total profit ₹27,600 ÷ 40 units = ₹690 per unit.

C's share = 12 units × ₹690 = ₹8,280.

∴ The correct answer is ₹8,280.

Alternate Method

Given:

Ratio A : B = 18 : 6 = 3 : 1

Ratio B : C = 7 : 12

Total Profit = ₹27,600

Calculations:

⇒ To equalize B, multiply A : B by 7: (3 × 7) : (1 × 7) = 21 : 7

⇒ Combined Ratio A : B : C = 21 : 7 : 12

⇒ Sum of ratio terms = 21 + 7 + 12 = 40

⇒ C's share = (12 ÷ 40) × 27,600

⇒ C's share = 12 × 690

⇒ C's share = ₹8,280

∴ The correct answer is ₹8,280.

Additional Information

Partnership Profit Distribution

Profit is distributed in the ratio of (Capital × Time). If time is constant, profit ratio equals the capital ratio.

Combining Ratios

If A:B = a:b and B:C = c:d, then A:B:C = (a×c) : (b×c) : (b×d).

Ratio to Value Conversion

Value of a part = (Ratio of that part ÷ Sum of all ratios) × Total Value.

Shortcut Trick

Remaining Distance = 1/3 of 132 km = 44 km.

Remaining Time = 4/7 of 14 hours = 8 hours.

Required Speed = 44 ÷ 8 = 5.5 km/hr.

∴ The correct answer is 5.5 km/hr.

Alternate Method

Given: Total Distance = 132 km, Total Time = 14 hours.

Step 1: Calculate Remaining Distance

⇒ Distance covered = 2/3 × 132 = 88 km

⇒ Remaining Distance = 132 − 88 = 44 km

Step 2: Calculate Remaining Time

⇒ Time taken = 3/7 × 14 = 6 hours

⇒ Remaining Time = 14 − 6 = 8 hours

Step 3: Calculate Required Speed

⇒ Speed = Distance ÷ Time

⇒ Speed = 44 ÷ 8 = 5.5 km/hr

∴ The correct answer is 5.5 km/hr.

Additional Information

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. In this case, 132 ÷ 14 ≈ 9.42 km/hr.

Uniform Speed Relationship

Distance = Speed × Time. To find any one parameter, the other two must be known or expressed in terms of a single variable.

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

Increase in average = (New Score − Old Average) ÷ Total Innings after new score

Increase = (183 − 52) ÷ 13

Increase = 131 ÷ 13 = 10.0769...

Rounding to the nearest whole number ≈ 10.

∴ The correct answer is 10.

Alternate Method

Given:

Average score in 12 innings = 52 runs

Score in 13^th innings = 183 runs

Formula Used:

Average = Total runs ÷ Number of innings

Calculations:

⇒ Total runs in 12 innings = 12 × 52 = 624 runs

⇒ Total runs after 13 innings = 624 + 183 = 807 runs

⇒ New average = 807 ÷ 13

⇒ New average = 62.0769... runs

⇒ Increase in average = New average − Old average

⇒ Increase = 62.0769... − 52 = 10.0769... runs

⇒ Rounding to the nearest whole number, we get 10.

∴ The correct answer is 10.

Additional Information

Average Change Concept

When a new observation is added, the change in average is equal to the difference between the new value and the old average, divided by the new total count of observations.

Rounding Off Rules

If the decimal part is 0.5 or greater, round up to the next whole number; if it is less than 0.5, round down to the current whole number.

Total Sum Formula

Total Sum = Average × Number of items. This is used to find the new sum when an entry is added or removed.

Shortcut Trick

Total distance to cover = Sum of lengths of both trains = 968 + 968 = 1936 m.

Relative speed (opposite direction) = Sum of individual speeds = 2 × Speed (since speeds are same).

Relative Speed = Total Distance ÷ Time = 1936 ÷ 22 = 88 m/s.

Speed of each train = 88 ÷ 2 = 44 m/s.

∴ The correct answer is 44 m/s.

Alternate Method

Given:

Length of Train 1 (L₁) = 968 m

Length of Train 2 (L₂) = 968 m

Time taken to cross each other (t) = 22 seconds

Speed of each train = s (since speeds are the same)

Formula Used:

Relative Speed = (Total Distance) ÷ (Total Time)

When two objects move in opposite directions, Relative Speed = s₁ + s₂

Calculations:

⇒ Total Distance = L₁ + L₂ = 968 + 968 = 1936 m

⇒ Relative Speed = s + s = 2s

⇒ 2s = 1936 ÷ 22

⇒ 2s = 88

⇒ s = 88 ÷ 2

⇒ s = 44 m/s

∴ The correct answer is 44 m/s.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds (s₁ − s₂).

Unit Conversion

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

Crossing a Stationary Object

When a train crosses a pole or a person, the distance covered is equal to the length of the train.

Shortcut Trick

A number is divisible by 3 if the sum of its digits is divisible by 3.

Option (1): 7 + 8 + 1 = 16 (No)

Option (2): 1 + 2 + 3 = 6 (Yes, 6 is divisible by 3)

Option (3): 2 + 4 + 5 = 11 (No)

Option (4): 5 + 5 + 7 = 17 (No)

∴ The correct answer is 123.

Alternate Method

Given: Numbers 781, 123, 245, 557.

Rule: Divisibility by 3 depends on the sum of digits.

⇒ For 781: Sum = 7 + 8 + 1 = 16; 16 ÷ 3 = 5 Remainder 1.

⇒ For 123: Sum = 1 + 2 + 3 = 6; 6 ÷ 3 = 2 Remainder 0.

⇒ For 245: Sum = 2 + 4 + 5 = 11; 11 ÷ 3 = 3 Remainder 2.

⇒ For 557: Sum = 5 + 5 + 7 = 17; 17 ÷ 3 = 5 Remainder 2.

∴ The correct answer is 123.

Additional Information

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility by 6

A number is divisible by 6 if it is even and the sum of its digits is divisible by 3.

Divisibility by 4

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

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is given by (100 − D%) : (100 + P%).

Let CP = 100, then MP = 100 + 80 = 180.

Profit = 8%, so Selling Price (SP) = 100 + 8 = 108.

Discount = MP − SP = 180 − 108 = 72.

X = (Discount ÷ MP) × 100 = (72 ÷ 180) × 100 = 40%.

∴ The correct answer is 40.

Alternate Method

Given → Markup% = 80%, Profit% = 8%, Discount% = X%.
Formulas: SP = CP × (100 + P%) ÷ 100 | SP = MP × (100 − D%) ÷ 100 | MP = CP × (100 + Markup%) ÷ 100.

⇒ Let Cost Price (CP) be 100.
⇒ Marked Price (MP) = 100 + 80% of 100 = 180.
⇒ Selling Price (SP) = 100 + 8% of 100 = 108.
⇒ Discount Amount = MP − SP = 180 − 108 = 72.
⇒ Discount Percentage (X) = (72 ÷ 180) × 100 = 40.

∴ The correct answer is 40.

Additional Information

Relation between CP, MP, Profit, and Discount

The formula CP × (1 + Markup%) × (1 − Discount%) = CP × (1 + Profit%) allows solving for any single unknown variable when others are provided.

Marked Price

It is the price displayed on the product label. Discounts are always calculated on the Marked Price (MP), while Profit or Loss is calculated on the Cost Price (CP).

Shortcut Trick

Use the Successive Multiplying Factor method.

Net Multiplier = 0.70 × 0.75 × 0.55 × 1.45

Net Multiplier = 0.525 × 0.7975 = 0.4186875

Decrease % = (1 − 0.4186875) × 100 = 58.13125%

∴ The correct answer is a decrease of 58.13%.

Alternate Method

Assume the original price of fuel is 100 units.

⇒ Price after 1^st month = 100 × (100 − 30)/100 = 70

⇒ Price after 2^nd month = 70 × (100 − 25)/100 = 70 × 0.75 = 52.5

⇒ Price after 3^rd month = 52.5 × (100 − 45)/100 = 52.5 × 0.55 = 28.875

⇒ Price after 4^th month = 28.875 × (100 + 45)/100 = 28.875 × 1.45 = 41.86875

⇒ Net decrease = 100 − 41.86875 = 58.13125

⇒ Percentage decrease = (58.13125 / 100) × 100 ≈ 58.13%

∴ The correct answer is a decrease of 58.13%.

Additional Information

Successive Percentage Change

For two successive changes a% and b%, the net change is given by [a + b + (ab/100)]%.

Multiplying Factor (MF)

For an x% increase, MF = (1 + x/100). For an x% decrease, MF = (1 − x/100). Final Value = Initial Value × MF₁ × MF₂ ...

Percentage Decrease Formula

Percentage Decrease = [(Initial Value − Final Value) / Initial Value] × 100%.