Quantitative Aptitude PYQs

Shortcut Trick

Solve brackets and multiplication first: (29 + 15) × 2 = 44 × 2 = 88.

Simplify the rest by grouping positive and negative terms.

Calculation: (66 + 48 + 84) − (88 + 33) = 198 − 121 = 77.

∴ The correct answer is 77.

Alternate Method

Given: 66 + 48 − (29 + 15) × 2 + 84 − 33

Apply the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction):

⇒ 66 + 48 − (44) × 2 + 84 − 33

⇒ 66 + 48 − 88 + 84 − 33

⇒ 114 − 88 + 84 − 33

⇒ 26 + 84 − 33

⇒ 110 − 33

⇒ 77

∴ The correct answer is 77.

Additional Information

BODMAS Rule

It is the standard order of operations: Brackets first, then Orders (exponents), followed by Division and Multiplication (left to right), and finally Addition and Subtraction (left to right).

Addition and Subtraction Priority

According to the BODMAS rule, addition and subtraction have the same priority level and are generally performed from left to right as they appear in the expression.

Shortcut Trick

Evaluate the Of and Multiplication first: 18 of 2 = 36 and 31 × 1 = 31.

Sum positive terms: 89 + 31 + 36 + 27 = 183.

Sum negative terms: 42 + 19 = 61.

Subtract negative sum from positive sum: 183 − 61 = 122.

∴ The correct answer is 122.

Alternate Method

Given Expression: 89 − 42 + 31 × 1 + (18 of 2) + 27 − 19

Applying the BODMAS rule (Bracket, Of, Division, Multiplication, Addition, Subtraction):

⇒ 89 − 42 + 31 × 1 + 36 + 27 − 19 (Evaluating Of: 18 × 2 = 36)

⇒ 89 − 42 + 31 + 36 + 27 − 19 (Evaluating Multiplication: 31 × 1 = 31)

⇒ (89 + 31 + 36 + 27) − 42 − 19 (Grouping Addition terms)

⇒ 183 − 42 − 19

⇒ 183 − 61 (Performing Subtraction)

⇒ 122

∴ The correct answer is 122.

Additional Information

BODMAS Rule

It defines the order of operations: Brackets, Of (Orders), Division, Multiplication, Addition, and Subtraction.

The 'Of' Operator

In mathematical expressions, 'Of' signifies multiplication and is prioritized higher than standard division and multiplication operations.

Sign Convention

When adding or subtracting multiple numbers, it is often easier to group all positive terms together and all negative terms together before finding the final result.

Shortcut Trick

Rewrite 8 × (4.5)³ as 2³ × (4.5)³ = (2 × 4.5)³ = 9³.

Numerator: 9³ − 1 = 729 − 1 = 728.

Denominator: 10² − 9 = 100 − 9 = 91.

Final result = 728 ÷ 91 = 8.

∴ The correct answer is 8.

Alternate Method

Given: Expression = (8 × (4.5)³ − 1) ÷ (10² − 9)

Method: Step-by-step simplification following BODMAS rules and Power Properties.

⇒ Numerator = 8 × (4.5)³ − 1

⇒ 8 × 91.125 − 1

⇒ 729 − 1 = 728

⇒ Denominator = 10² − 9

⇒ 100 − 9 = 91

⇒ Final Expression = 728 ÷ 91

⇒ 8

∴ The correct answer is 8.

Additional Information

BODMAS Rule

It stands for Brackets, Orders (Powers/Roots), Division, Multiplication, Addition, and Subtraction, defining the correct sequence for mathematical operations.

Power Property

The rule aⁿ × bⁿ = (a × b)ⁿ allows multiplying bases when the exponents are identical, simplifying complex terms like 2³ × 4.5³.

Algebraic Identity (a³ − b³)

The difference of cubes is given by (a − b)(a² + ab + b²), which can be useful for simplifying expressions involving cubic terms.

Shortcut Trick

Find the square root of 2025, which is 45.

Simplify the ratio: √x = 100 ÷ 45 = 20 ÷ 9.

Squaring both sides to find x: (20 ÷ 9)² = 400 ÷ 81.

∴ The correct answer is 400/81.

Alternate Method

Given:

√x = 100 ÷ √2025

Calculation:

⇒ √x = 100 ÷ 45

⇒ √x = (20 × 5) ÷ (9 × 5)

⇒ √x = 20 ÷ 9

Squaring both sides of the equation:

⇒ (√x)² = (20 ÷ 9)²

⇒ x = 20² ÷ 9²

⇒ x = 400 ÷ 81

∴ The correct answer is 400/81.

Additional Information

Square Root of Numbers Ending in 25

For a number ending in 25, the square root ends in 5. The remaining digits are the product of two consecutive integers (e.g., 20 = 4 × 5, so √2025 = 45).

Power of a Quotient

According to laws of indices, (a ÷ b)ⁿ = aⁿ ÷ bⁿ. This is used when squaring fractions to find the value of x.

Isolating the Variable

To solve for a variable inside a radical, apply the inverse operation (squaring for square roots) to both sides of the equation.

Shortcut Trick

Use the property: 1/(√a − √b) = (√a + √b) / (a − b).

Here, a = 6 and b = 2, so 1/(√6 − √2) = (√6 + √2) / 4.

Total = (√6 + √2) + (√6 + √2) / 4 = (1 + 1/4) × (√6 + √2) = 5/4 (√6 + √2).

∴ The correct answer is 5/4 (√6 + √2).

Alternate Method

Given expression: (√6 + √2) + 1/(√6 − √2)

To solve this, we will perform Rationalization of the Denominator for the second term.

⇒ 1/(√6 − √2) = [1 × (√6 + √2)] / [(√6 − √2) × (√6 + √2)]

⇒ Using Identity (a − b)(a + b) = a² − b² in the denominator:

⇒ 1/(√6 − √2) = (√6 + √2) / [(√6)² − (√2)²]

⇒ 1/(√6 − √2) = (√6 + √2) / (6 − 2) = (√6 + √2) / 4

⇒ Now, substitute this back into the original expression:

⇒ Result = (√6 + √2) + (√6 + √2) / 4

⇒ Result = [4 × (√6 + √2) + 1 × (√6 + √2)] / 4

⇒ Result = 5(√6 + √2) / 4 = 5/4 (√6 + √2)

∴ The correct answer is 5/4 (√6 + √2).

Additional Information

Rationalizing Factor

The Conjugate of a binomial surd like (√x − √y) is (√x + √y). Multiplying them removes the square root from the denominator.

Algebraic Identity for Surds

The formula (a − b)(a + b) = a² − b² is essential for simplifying fractions involving Square Roots.

Simplified Form

Always check if terms can be combined by taking a common factor after rationalization to reach the final Simplified Value.

Shortcut Trick

The diagonal of a square is directly proportional to its side.

Diagonal = Side × √2

Given Side = 10 cm.

Diagonal = 10 × √2 = 10√2 cm.

∴ The correct answer is 10√2 cm.

Alternate Method

Given:

Side of the square (a) = 10 cm

Formula Used:

According to Pythagoras Theorem in a square, the diagonal (d) forms the hypotenuse of a right-angled triangle with two sides (a).

d² = a² + a² ⇒ d = √(2a²) = a√2

Calculations:

⇒ Side (a) = 10 cm

⇒ Diagonal (d) = √(10² + 10²)

⇒ d = √(100 + 100)

⇒ d = √200

⇒ d = √(100 × 2)

⇒ d = 10√2 cm

∴ The correct answer is 10√2 cm.

Additional Information

Area of a Square

The area can be calculated using the side as Area = a² or using the diagonal as Area = d² ÷ 2.

Perimeter of a Square

The total boundary length is given by Perimeter = 4 × side.

Relation with Circle

For a square inscribed in a circle, the diagonal of the square is equal to the diameter of the circle.

Shortcut Trick

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

Sum of digits of 95P9 = 9 + 5 + P + 9 = 23 + P.

Testing the options for P, we find that 23 + 7 = 30, which is divisible by 3.

∴ The correct answer is 7.

Alternate Method

Given: The four-digit number 95P9 is exactly divisible by 3.

Divisibility Rule of 3: The sum of all the individual digits of the number must be divisible by 3.

⇒ Sum = 9 + 5 + P + 9

⇒ Sum = 23 + P

⇒ For the number to be divisible by 3, (23 + P) must be 24, 27, 30, 33, etc.

⇒ If 23 + P = 24, then P = 1 (Not in options)

⇒ If 23 + P = 27, then P = 4 (Not in options)

⇒ If 23 + P = 30, then P = 7 (Present in options)

⇒ If 23 + P = 33, then P = 10 (Not a single digit)

∴ The correct answer is 7.

Additional Information

Divisibility Rule of 9

A number is divisible by 9 if the sum of its digits is divisible by 9. Every number divisible by 9 is also divisible by 3.

Divisibility Rule of 6

A number is divisible by 6 if it is even (ends in 0, 2, 4, 6, or 8) and is also divisible by 3.

Divisibility Rule of 4

A number is divisible by 4 if the last two digits of the number are divisible by 4 or if the last two digits are 00.

Shortcut Trick

Apply Pythagorean Triplets logic: (3, 4, 5) scaled by factor 3.

Given Length = 9 cm (3 × 3) and Diagonal = 15 cm (5 × 3).

The missing side Breadth must be (4 × 3) = 12 cm.

Required Ratio = Length : Breadth = 9 : 12 = 3 : 4.

∴ The correct answer is 3 : 4.

Alternate Method

Given:

Length (l) of the rectangle = 9 cm

Diagonal (d) of the rectangle = 15 cm

Formula Used:

In a rectangle, d² = l² + b² (where b is the breadth).

Calculations:

⇒ (15)² = (9)² + b²

⇒ 225 = 81 + b²

⇒ b² = 225 − 81

⇒ b² = 144

⇒ b = √144 = 12 cm

⇒ Ratio of Length to Breadth = l : b

⇒ Ratio = 9 : 12

⇒ Ratio = 3 : 4

∴ The correct answer is 3 : 4.

Additional Information

Properties of a Rectangle

Opposite sides are equal and parallel, and each internal angle is 90°.

Area and Perimeter

Area = Length × Breadth | Perimeter = 2 × (Length + Breadth).

Pythagorean Theorem

For a right-angled triangle, a² + b² = c², where c is the hypotenuse (diagonal in a rectangle).

Shortcut Trick

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

Identify a = 460 and b = 240.

Substituting the values: (460 − 240)² = 220².

Calculating the square: 220 × 220 = 48400.

∴ The correct answer is 48400.

Alternate Method

Given: (460 + 240)² − 4 × 460 × 240

Method: Step-by-step simplification using BODMAS rules.

⇒ (700)² − 4 × 460 × 240

⇒ 490000 − 4 × 110400

⇒ 490000 − 441600

⇒ 48400

∴ The correct answer is 48400.

Additional Information

Square of the Sum Identity

The algebraic expansion is (a + b)² = a² + 2ab + b².

Square of the Difference Identity

The algebraic expansion is (a − b)² = a² − 2ab + b².

Relationship between Identities

The difference between the two squares is given by (a + b)² − (a − b)² = 4ab.

Shortcut Trick

If the Average age remains unchanged after some members leave, the Average age of those leaving members must be equal to the Original Average.

Average age of 2 leaving boys = 19 years

Sum of ages of 2 leaving boys = 2 × 19 = 38 years

Value of x = 38 − 21 = 17

∴ The correct answer is 17.

Alternate Method

Given: Initial Average = 19, Number of boys = 28, Boys leaving = 2, Final Average = 19.

Formula Used: Total Age = Average × Number of persons

⇒ Total Age of 28 boys = 28 × 19 = 532 years

⇒ Remaining boys in the class = 28 − 2 = 26 boys

⇒ Total Age of 26 boys = 26 × 19 = 494 years

⇒ Sum of ages of 2 boys who left = (Total age of 28) − (Total age of 26)

⇒ x + 21 = 532 − 494

⇒ x + 21 = 38

⇒ x = 38 − 21 = 17

∴ The correct answer is 17.

Additional Information

Average Formula

The Average of a set of observations is the sum of the observations divided by the total number of observations. Average = Sum ÷ Count.

Replacement Rule

If a person leaves and is replaced by another, New Average = Old Average + (Age Gain/Loss ÷ Total Count).

Weighted Average

When two groups with different averages are combined, Combined Average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Shortcut Trick

To find the least number exactly divisible by 5, 7, 9, and 21, we calculate their LCM.

Since 7 is a factor of 21, the LCM of (5, 7, 9, 21) is equivalent to the LCM of (5, 9, 21).

Multiply the largest number 21 by the prime factors of other numbers not already present in it.

LCM = 21 × 3 (remaining factor of 9) × 5 (factor of 5) = 63 × 5 = 315.

∴ The correct answer is 315.

Alternate Method

Given: The set of numbers is 5, 7, 9, and 21.

Formula Used: The Least Common Multiple (LCM) is the product of the highest powers of all prime factors involved in the numbers.

⇒ Prime factors of 5 = 5¹

⇒ Prime factors of 7 = 7¹

⇒ Prime factors of 9 = 3 × 3 = 3²

⇒ Prime factors of 21 = 3 × 7 = 3¹ × 7¹

⇒ LCM = 3² × 5¹ × 7¹

⇒ LCM = 9 × 5 × 7

⇒ LCM = 315

∴ The correct answer is 315.

Additional Information

LCM and HCF Relation

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

LCM of Prime Numbers

The Least Common Multiple of a set of prime numbers is simply the product of those numbers.

Divisibility Rule of 9

A number is divisible by 9 if the sum of its individual digits is a multiple of 9. For 315: 3 + 1 + 5 = 9, which is divisible by 9.

Shortcut Trick

Find the differences between the given numbers: (50 − 38), (74 − 50), and (98 − 74).

Differences are 12, 24, and 24.

The HCF (Highest Common Factor) of 12, 24, and 24 is 12.

Thus, 12 is the largest number that leaves the same remainder (2) in each case.

∴ The correct answer is 12.

Alternate Method

Given: The numbers are 38, 50, 74, and 98.

Formula: To find the largest number that divides several numbers leaving the same remainder, find the HCF of the absolute differences between the numbers.

⇒ First difference = |50 − 38| = 12

⇒ Second difference = |74 − 50| = 24

⇒ Third difference = |98 − 74| = 24

⇒ Required Number = HCF of (12, 24, 24)

⇒ Factors of 12 = 1, 2, 3, 4, 6, 12

⇒ Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

⇒ Common Factors = 1, 2, 3, 4, 6, 12

⇒ Highest Common Factor (HCF) = 12

∴ The correct answer is 12.

Additional Information

HCF with Specific Remainders

To find the largest number that divides A, B, and C leaving remainders x, y, and z respectively, find the HCF of (A − x), (B − y), and (C − z).

LCM with Same Remainder

The smallest number which when divided by x, y, and z leaves the same remainder 'r' in each case is [LCM(x, y, z) + r].

HCF Property

The HCF of a set of numbers always divides the difference between any two numbers in that set.

Shortcut Trick

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

Given Profit percentage = 7%, which corresponds to the difference of ₹385.

⇒ 7% of CP = ₹385

⇒ 1% of CP = 385 ÷ 7 = ₹55

⇒ 100% of CP = 55 × 100 = ₹5500

∴ The correct answer is ₹5500.

Alternate Method

Given:

Difference (SP − CP) = ₹385

Profit percentage = 7%

Formula Used:

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

Calculations:

⇒ Profit = Selling Price − Cost Price = ₹385

⇒ Profit % = (Profit ÷ CP) × 100

⇒ 7 = (385 ÷ CP) × 100

⇒ CP = (385 × 100) ÷ 7

⇒ CP = 55 × 100

⇒ CP = ₹5500

∴ The correct answer is ₹5500.

Additional Information

Relationship between SP and CP

Selling Price (SP) = CP × (100 + Profit%) ÷ 100. If there is a loss, SP = CP × (100 − Loss%) ÷ 100.

Cost Price Calculation

When the difference between SP and CP is known (Profit or Loss), CP = (Difference ÷ Profit/Loss %) × 100.

Marked Price and Discount

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

Shortcut Trick

Effective percentage = 70% × 60% = 42%

According to the question, 42% of the number = 420

Dividing both sides by 4.2 gives 10% of the number = 100

∴ The correct answer is 100.

Alternate Method

Given: 70 percent of 60 percent of a number is 420.

Formula Used: Value = (P₁ ÷ 100) × (P₂ ÷ 100) × Total Number

⇒ Let the number be x.

⇒ (70 ÷ 100) × (60 ÷ 100) × x = 420

⇒ 0.42 × x = 420

⇒ x = 420 ÷ 0.42

⇒ x = 1000

⇒ 10 percent of x = (10 ÷ 100) × 1000

⇒ 10 percent of 1000 = 100

∴ The correct answer is 100.

Additional Information

Product of Percentages

When multiple percentages are applied to a single number, they can be multiplied together to find the effective percentage: a% of b% = (a × b) ÷ 100%.

Fractional Equivalents

Using fractions like 7/10 for 70% and 3/5 for 60% often simplifies complex multiplication and division in competitive exams.

Base Value Conversion

To find the original 100% value from a known percentage P, use the formula: Total = (Given Value × 100) ÷ P.

Shortcut Trick

Calculate Cost Price (CP) = Selling Price (SP) + Loss

CP = 2300 + 200 = 2500

Loss Percentage = (Loss ÷ CP) × 100

Loss % = (200 ÷ 2500) × 100 = 8%

∴ The correct answer is 8%.

Alternate Method

Given:

Selling Price (SP) = ₹2300

Value of Loss = ₹200

Formula Used:

1. Cost Price (CP) = Selling Price (SP) + Loss
2. Loss Percentage = (Loss ÷ Cost Price) × 100

Calculations:

⇒ CP = 2300 + 200

⇒ CP = ₹2500

⇒ Loss % = (200 ÷ 2500) × 100

⇒ Loss % = 200 ÷ 25

⇒ Loss % = 8%

∴ The correct answer is 8%.

Additional Information

Profit and Loss Percentage

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

Relation between CP and SP

When there is a loss, Selling Price (SP) = CP × (100 − Loss%) ÷ 100. When there is a profit, SP = CP × (100 + Profit%) ÷ 100.

Marked Price and Discount

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

Shortcut Trick

Assume Total Income = 100 parts, then Expenditure = 70 and Savings = 30.

Apply the weighted average concept: Total Change = (Change in Exp × Exp parts) + (Change in Sav × Sav parts).

30% × 100 = (x% × 70) + (40% × 30)

3000 = 70x + 1200 ⇒ 70x = 1800 ⇒ x = 180 ÷ 7 = 25.71%.

∴ The correct answer is 25.71 percent.

Alternate Method

Given: Initial spending = 70%, Income increase = 30%, Savings increase = 40%.

Formula Used: Income = Expenditure + Savings; % Change = ((New − Old) ÷ Old) × 100.

Let the initial Income be 100.

⇒ Initial Expenditure = 70% of 100 = 70

⇒ Initial Savings = 100 − 70 = 30

⇒ New Income = 100 + (30% of 100) = 130

⇒ New Savings = 30 + (40% of 30) = 30 + 12 = 42

⇒ New Expenditure = New Income − New Savings = 130 − 42 = 88

⇒ Increase in Expenditure = 88 − 70 = 18

⇒ Percentage Increase in Expenditure = (18 ÷ 70) × 100

⇒ % Increase = 180 ÷ 7 ≈ 25.71%

∴ The correct answer is 25.71 percent.

Additional Information

Income, Expenditure, and Savings Relationship

The fundamental relation is Income = Expenditure + Savings. Any change in one or more components must balance this equation.

Alligation Method for Income Problems

Percentage changes in Expenditure and Savings can be alligated to find the percentage change in Income, where the ratio of parts is Expenditure : Savings.

Percentage Change Formula

Percentage change is calculated as ((Final Value − Initial Value) ÷ Initial Value) × 100. Always ensure the base value used is the original (initial) value.

Shortcut Trick

Ratio of efficiency of A and B = 6 : 1

Combined efficiency of A and B = 6 + 1 = 7 units/day

Total work = Combined efficiency × Time = 7 × 18 = 126 units

Time taken by B alone = Total work ÷ Efficiency of B = 126 ÷ 1 = 126 days

∴ The correct answer is 126 days.

Alternate Method

Given that A is 6 times as efficient as B.

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

⇒ Efficiency of A = 6 × 1 = 6 units/day.

⇒ Total efficiency of (A + B) = 6 + 1 = 7 units/day.

⇒ Total work = Combined efficiency × Time taken together

⇒ Total work = 7 × 18 = 126 units.

⇒ Time taken by B alone = Total work ÷ Efficiency of B

⇒ Time = 126 ÷ 1 = 126 days.

∴ The correct answer is 126 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to time taken. If the efficiency ratio of two workers is x : y, the ratio of time taken to complete the same work is y :

x. Work and Wages

Wages are distributed in the ratio of the work done by each person, which is equivalent to the ratio of their efficiencies if they work for the same duration.

Combined Work Formula

If A can do work in x days and B in y days, they together finish the work in (x × y) ÷ (x + y) days.

Shortcut Trick

Use the Chain Rule formula: M₁ × D₁ × H₁ = M₂ × D₂ × H₂

Substitute the values: 50 × 30 × 6 = M₂ × 45 × 4

⇒ 9000 = M₂ × 180

⇒ M₂ = 9000 ÷ 180 = 50

∴ The correct answer is 50 men.

Alternate Method

Given:

Initial men (M₁) = 50

Initial days (D₁) = 30

Initial hours per day (H₁) = 6

Final days (D₂) = 45

Final hours per day (H₂) = 4

Formula Used:

For the same work (wall): M₁D₁H₁ = M₂D₂H₂

⇒ Total work in man-hours = M₁ × D₁ × H₁

⇒ Total work = 50 × 30 × 6 = 9000 man-hours

⇒ Required men × 45 × 4 = 9000

⇒ M₂ × 180 = 9000

⇒ M₂ = 9000 ÷ 180

⇒ M₂ = 50 men

∴ The correct answer is 50 men.

Additional Information

The General Chain Rule

When work (W) and efficiency (E) are different, use the complete formula: (M₁ × D₁ × H₁ × E₁) ÷ W₁ = (M₂ × D₂ × H₂ × E₂) ÷ W₂.

Inverse Proportion in Work

The number of men is inversely proportional to the days and hours taken to complete a constant amount of work.

Man-Days Concept

Total work is often measured in Man-Days or Man-Hours, representing the effort of one person working for one day or one hour respectively.

Shortcut Trick

Relative Speed = Total distance ÷ Time taken

Total distance = 300 + 500 = 800 m

Relative Speed = 800 ÷ 10 = 80 m/s

Speed of Train B = Relative Speed − Speed of Train A = 80 − 20 = 60 m/s

∴ The correct answer is 60 m/s.

Alternate Method

Given:

Length of Train A (L_A) = 300 m

Length of Train B (L_B) = 500 m

Speed of Train A (S_A) = 20 m/s

Time taken (T) = 10 s

Formula Used:

When two trains cross each other in opposite directions:

Relative Speed = S_A + S_B = (L_A + L_B) ÷ T

Calculations:

⇒ Total distance = 300 + 500 = 800 m

⇒ S_A + S_B = 800 ÷ 10

⇒ 20 + S_B = 80

⇒ S_B = 80 − 20

⇒ S_B = 60 m/s

∴ The correct answer is 60 m/s.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction at speeds u and v ( v), the relative speed is (u − v).

Speed Conversion

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

Crossing a Point Object

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

Shortcut Trick

Initial Speed = (48 ÷ 72) × 60 = 40 km/hr.

New Speed = 40 − 10 = 30 km/hr.

Ratio of Speed = 40 : 30 = 4 : 3.

For constant Distance, Time is inversely proportional to Speed ⇒ Time Ratio = 3 : 4.

3 units = 72 min ⇒ 1 unit = 24 min ⇒ 4 units = 4 × 24 = 96 min.

∴ The correct answer is 96 min.

Alternate Method

Given:

Distance = 48 km

Initial Time (T₁) = 72 min = 72/60 hr = 1.2 hr

Speed reduction = 10 km/hr

Formula Used:

Speed = Distance ÷ Time

Time = Distance ÷ Speed

Calculations:

⇒ Initial Speed (S₁) = 48 ÷ 1.2 = 40 km/hr

⇒ New Speed (S₂) = 40 − 10 = 30 km/hr

⇒ New Time (T₂) = Distance ÷ S₂

⇒ T₂ = 48 ÷ 30 hr

⇒ T₂ (in min) = (48 ÷ 30) × 60

⇒ T₂ = 48 × 2 = 96 min

∴ The correct answer is 96 min.

Additional Information

Unit Conversion

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

Inversely Proportional Logic

If Distance is constant, Speed₁ × Time₁ = Speed₂ × Time₂. This allows solving for any variable without finding actual distance.

Average Speed

If a car covers two equal distances at speeds x and y, the Average Speed = 2xy ÷ (x + y).