Quantitative Aptitude PYQs

Shortcut Trick

Average Speed = Total Distance ÷ Total Time

Total Distance = 684 + 1078 + 2198 = 3960 m

Total Time = 19 + 22 + 31 = 72 min

Average Speed = 3960 ÷ 72 = 55 m/min

∴ The correct answer is 55 m/min.

Alternate Method

Given:

Distances (d₁, d₂, d₃) = 684 m, 1078 m, 2198 m

Time intervals (t₁, t₂, t₃) = 19 min, 22 min, 31 min

Formula Used:

Average Speed = (d₁ + d₂ + d₃) ÷ (t₁ + t₂ + t₃)

Calculations:

⇒ Total Distance = 684 + 1078 + 2198 = 3960 m

⇒ Total Time = 19 + 22 + 31 = 72 min

⇒ Average Speed = 3960 ÷ 72

⇒ Average Speed = 55 m/min

∴ The correct answer is 55 m/min.

Additional Information

Average Speed Formula

It is defined as the total distance traveled divided by the total time taken. V_avg = Total Distance ÷ Total Time.

Equal Distance Case

If two equal distances are covered at speeds x and y, then Average Speed = 2xy ÷ (x + y).

Unit Conversion

To convert m/sec to km/hr, multiply by 18/5. To convert m/min to m/sec, divide by 60.

Shortcut Trick

The number of diagonals in a regular polygon with n sides is calculated using the direct formula:

Number of diagonals = [n × (n − 3)] ÷ 2

Given: n = 37

⇒ Diagonals = [37 × (37 − 3)] ÷ 2

⇒ Diagonals = [37 × 34] ÷ 2 = 37 × 17 = 629

∴ The correct answer is 629 diagonals.

Alternate Method

Given:

Number of sides (n) = 37

Formula Used:

Number of diagonals = ⁿC₂ − n

(This formula represents choosing any 2 vertices out of n to form a line segment, and then subtracting the n segments that are actually sides of the polygon.)

        A B C D E (Illustration: Pentagon with 5 diagonals shown in red) </

Shortcut Trick

Net percentage change formula = x + y + (x × y)/100

Here, x = −10% (reduction) and y = +10% (increase)

Net change = −10 + 10 + (−10 × 10)/100 = −1%

Final Price = 25,000 × (100 − 1)/100 = 25,000 × 0.99 = ₹24,750

∴ The correct answer is ₹24,750.

Alternate Method

Given:

Initial Price = ₹25,000

Reduction in 1^st year = 10%

Increase in 2^nd year = 10%

Calculations:

⇒ Price after 1^st year = 25,000 − (10% of 25,000)

⇒ Price after 1^st year = 25,000 − 2,500 = ₹22,500

⇒ Price after 2^nd year = 22,500 + (10% of 22,500)

⇒ Price after 2^nd year = 22,500 + 2,250 = ₹24,750

∴ The correct answer is ₹24,750.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the effective change is [x + y + (xy/100)]%.

Same Percent Increase and Decrease

If a value is increased by x% and then decreased by x%, there is always a net decrease of (x²/100)%.

Base Change Principle

The second percentage change is always calculated on the new (updated) base value, not the initial value.

Shortcut Trick

Effective Cost Price = 500 + 50 = ₹550.

Profit% = 10% ⇒ Multiplier = (100 + 10) ÷ 100 = 1.1.

Selling Price = 550 × 1.1 = ₹605.

∴ The correct answer is ₹605.

Alternate Method

Given: Cost Price (CP) = ₹500, Overhead Expenses = ₹50, Profit% = 10%.

Formulas: Total CP = Purchase Price + Overhead | SP = Total CP × (100 + Profit%) ÷ 100

⇒ Total CP = 500 + 50 = ₹550.

⇒ Profit Amount = 10% of 550 = (10 ÷ 100) × 550 = ₹55.

⇒ Selling Price (SP) = Total CP + Profit = 550 + 55 = ₹605.

∴ The correct answer is ₹605.

Additional Information

Overhead Expenses

Any extra amount spent on repairs, packaging, or transport is added to the initial CP to find the Effective Cost Price.

Profit Percentage

Profit% is always calculated on the Total Cost Price unless stated otherwise. Formula: Profit% = (Profit ÷ Total CP) × 100.

Shortcut Trick

Use the value substitution method by choosing values that satisfy the condition x + y + z = 0 (where none of them is 0).

Let x = 1, y = 1, and z = −2.

Substitute these values into the given expression:

⇒ (1² ÷ (1 × (−2))) + (1² ÷ ((−2) × 1)) + ((−2)² ÷ (1 × 1))

⇒ −1/2 − 1/2 + 4

⇒ −1 + 4 = 3

∴ The correct answer is 3.

Alternate Method

Given:

x + y + z = 0

Formula Used:

If x + y + z = 0, then the algebraic identity is x³ + y³ + z³ = 3xyz.

Calculations:

The expression to find is:

⇒ (x² ÷ yz) + (y² ÷ zx) + (z² ÷ xy)

Take the LCM of the denominators (yz, zx, xy) which is xyz:

⇒ (x³ + y³ + z³) ÷ xyz

Substitute x³ + y³ + z³ = 3xyz into the numerator:

⇒ 3xyz ÷ xyz

⇒ 3

∴ The correct answer is 3.

Additional Information

Standard Algebraic Identity

The sum of cubes formula is given by: x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − xy − yz − zx).

Conditional Identity

When x + y + z = 0, the right-hand side of the standard identity becomes zero, which simplifies the equation directly to x³ + y³ + z³ = 3xyz.

Sum of Squares Identity

The term (x² + y² + z² − xy − yz − zx) can also be written in the form (1/2) × [(x − y)² + (y − z)² + (z − x)²].

Shortcut Trick

Overall percentage increase = (11718 − 10500) ÷ 10500 × 100 = 1218 ÷ 105 = 11.6%

Using Alligation: Males (10%) and Females (15%) with mean (11.6%) gives ratio (15 − 11.6) : (11.6 − 10) = 3.4 : 1.6 = 17 : 8.

Total ratio parts = 17 + 8 = 25 units → 10500. So, 1 unit = 420.

Difference = 17 − 8 = 9 units → 9 × 420 = 3780.

∴ The correct answer is 3780.

Alternate Method

Given: Initial population = 10500, Final population = 11718, Male increase = 10%, Female increase = 15%.

⇒ Total increase = 11718 − 10500 = 1218

⇒ Overall % increase = (1218 ÷ 10500) × 100 = 11.6%

⇒ Male (M) : Female (F) ratio by alligation = (15 − 11.6) : (11.6 − 10) = 3.4 : 1.6 = 17 : 8

⇒ Total units = 17 + 8 = 25 units

⇒ 25 units = 10500 ⇒ 1 unit = 420

⇒ Difference in population = (17 − 8) × 420 = 9 × 420 = 3780

∴ The correct answer is 3780.

Additional Information

Alligation Rule

It is used to find the ratio in which two components are mixed to get a desired mean value: (Quantity 1 / Quantity 2) = (Value 2 − Mean) / (Mean − Value 1).

Percentage Change

Percentage Change = [(New Value − Original Value) / Original Value] × 100. This is the base for finding the mean in population problems.

Ratio to Actual Value

If a total amount T is divided in ratio a:b, then the difference between parts is |a − b| ÷ (a + b) × T.

Shortcut Trick

In a proportion where x/a = b/x, the value of x is the geometric mean √(a × b).

x² = 34 × 306

x = √(34 × 34 × 9) = 34 × 3 = 102.

∴ The correct answer is 102.

Alternate Method

Given: Equation is ?/34 = 306/?

Formula Used: Cross-multiplication method: a/b = c/d ⇒ a × d = b × c

⇒ Let the unknown number be x.

⇒ x/34 = 306/x

⇒ x × x = 306 × 34

⇒ x² = 10404

⇒ x = √10404

⇒ x = 102

∴ The correct answer is 102.

Additional Information

Mean Proportional

If three numbers a, x, b are in continued proportion, then x is the mean proportional such that x = √(ab).

Square Root Shortcut

To find √10404, look at the last digit (4), meaning the root ends in 2 or 8. Since 100² = 10000, the answer must be slightly more than 100, which is 102.

Shortcut Trick

Total age after 5 years = 50 + (5 × 2) = 60 years.

Ratio after 5 years (Man : Son) = 3 : 1.

Total ratio parts = 3 + 1 = 4 parts.

Son's age after 5 years = 60 ÷ 4 = 15 years.

Son's present age = 15 − 5 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given: Sum of present ages = 50 years. Condition after 5 years = Man = 3 × Son.

Let the present age of the son be x years.

Let the present age of the man be (50 − x) years.

After 5 years:

⇒ Age of son = x + 5

⇒ Age of man = (50 − x) + 5 = 55 − x

According to the question:

⇒ 55 − x = 3 × (x + 5)

⇒ 55 − x = 3x + 15

⇒ 4x = 55 − 15

⇒ 4x = 40

⇒ x = 10

∴ The correct answer is 10 years.

Additional Information

Age Sum Property

If the sum of ages of 'n' people is 'S' now, then after 't' years, the sum will be S + (n × t).

Ratio Method for Ages

When a ratio and a total sum are known for the same time period, divide the sum by the total ratio parts to find the value of one unit.

Age Difference Constant

The difference between the ages of two people remains constant throughout their lives, regardless of the years passed.

Shortcut Trick

Apply the exponent rules directly: (a^m)ⁿ = a^mn and a^m ÷ aⁿ = a^m−n.

(2³)² ÷ 2⁴ = 2⁶ ÷ 2⁴

2⁶ ÷ 2⁴ = 2² = 4

∴ The correct answer is 4.

Alternate Method

Given:

Expression: (2³)² ÷ 2⁴

Formula Used:

Power of a Power Rule: (a^m)ⁿ = a^{m × n}

Quotient Rule for Exponents: a^m ÷ aⁿ = a^{m − n}

Calculations:

⇒ (2³)² ÷ 2⁴

⇒ 2^{3 × 2} ÷ 2⁴

⇒ 2⁶ ÷ 2⁴

⇒ 2^{6 − 4}

⇒ 2²

⇒ 4

∴ The correct answer is 4.

Additional Information

Product Rule for Exponents

When multiplying bases that are the same, add the exponents: a^m × aⁿ = a^m+n.

Negative Exponent Rule

A negative exponent indicates taking the reciprocal of the base: a^−m = 1 ÷ a^m.

Zero Exponent Rule

Any non-zero base raised to the power of zero is exactly equal to one: a⁰ = 1.

Power of a Product Rule

When a product is raised to a power, each factor is raised to that same power: (a × b)^m = a^m × b^m.

Shortcut Trick

Let the cost of one ball be B and one bat be T.

Given: 2B + 3T = 84 and 3B + 1T = 63.

To find 5B + 3T, we can observe that 5B + 3T = (2B + 3T) + 3B.

From the second equation, 3B = 63 − T. But solving for B: 3 × (3B + T) − (2B + 3T) = 3(63) − 84 ⇒ 7B = 105 ⇒ B = 15.

Substituting B in the goal: 5B + 3T = (2B + 3T) + 3B = 84 + 3(15) = 84 + 45 = 129.

∴ The correct answer is ₹ 129.

Alternate Method

Given:

Cost of 2 balls + 3 bats = ₹ 84

Cost of 3 balls + 1 bat = ₹ 63

Formula Used:

System of linear equations: Let cost of ball = x and bat = y.

⇒ 2x + 3y = 84 ... (Equation 1)

⇒ 3x + y = 63 ... (Equation 2)

⇒ From (2), y = 63 − 3x

⇒ Substitute y in (1): 2x + 3(63 − 3x) = 84

⇒ 2x + 189 − 9x = 84

⇒ −7x = 84 − 189

⇒ −7x = −105 ⇒ x = 15

⇒ y = 63 − 3(15) = 63 − 45 = 18

⇒ Cost of 5 balls and 3 bats = 5x + 3y

⇒ (5 × 15) + (3 × 18) = 75 + 54 = 129

∴ The correct answer is ₹ 129.

Additional Information

Linear Equations in Two Variables

Equations of the form ax + by = c, which can be solved using substitution, elimination, or cross-multiplication methods.

Elimination Method

Multiply equations by suitable constants so that the coefficients of one variable become equal, then add or subtract to eliminate it.

Unitary Method

Finding the value of a single unit (1 ball or 1 bat) first is often the most reliable way to calculate the cost of any combined set of items.

Shortcut Trick

Income is always 100%.

Savings % = 100% − Spending % = 100% − 50% = 50%.

Given Savings = ₹42,000 (unit value).

50% → ₹42,000

100% → ₹42,000 × 2 = ₹84,000

∴ The correct answer is ₹84,000.

Alternate Method

Given:

Spending = 50% of Income

Savings = ₹42,000

Formula Used:

Income = Expenditure + Savings

Income = Savings / (1 − Spending Fraction)

Let Total Income be x.

⇒ Expenditure = 50% of x = 0.5x

⇒ Savings = x − 0.5x = 0.5x

⇒ 0.5x = 42,000

⇒ x = 42,000 / 0.5

⇒ x = 42,000 × 2

⇒ x = 84,000

∴ The correct answer is ₹84,000.

Additional Information

Income-Expenditure Relationship

Income is always the sum of Expenditure and Savings. Ratio of Income : Expenditure : Savings is used for complex calculations.

Percentage Change in Income

If Income increases by a% and Expenditure increases by b%, the change in Savings depends on the initial ratio of E:S.

Fractional Conversions

50% = 1/2 | 25% = 1/4 | 33.33% = 1/3 | 20% = 1/5. Using fractions simplifies division steps.

Shortcut Trick

Arrange data: 6, 8, 9, 11, 16, 22

Total terms (n) = 6 (Even number)

Median = Average of the two middle terms

Middle terms are 9 and 11

Median = (9 + 11) ÷ 2 = 10

∴ The correct answer is 10.

Alternate Method

Given: Data set = 9, 6, 8, 11, 16, 22

Formula Used:

If n is even, Median = [ (n/2)^th term + (n/2 + 1)^th term ] ÷ 2

⇒ Step 1: Arrange data in ascending order: 6, 8, 9, 11, 16, 22

⇒ Step 2: Count the number of observations (n) = 6

⇒ Step 3: Identify the positions of the middle terms

⇒ Position 1 = n/2 = 6/2 = 3^rd term

⇒ Position 2 = (n/2) + 1 = 3 + 1 = 4^th term

⇒ Step 4: Value of 3^rd term = 9 and 4^th term = 11

⇒ Median = (9 + 11) ÷ 2

⇒ Median = 20 ÷ 2 = 10

∴ The correct answer is 10.

Additional Information

Median for Odd Number of Terms

If the total number of terms (n) is odd, the median is the middle-most term located at the ((n + 1)/2)^th position after sorting.

Arithmetic Mean

Mean is the sum of all values divided by the number of values. Formula: Σx ÷ n.

Mode of Data

Mode is the value that appears most frequently in the data set. A set can be unimodal, bimodal, or multimodal.

Relationship between Mean, Median, and Mode

For a moderately skewed distribution: Mode = 3 × Median − 2 × Mean.

Shortcut Trick

Divisibility rule of 4: The last two digits of the number must be divisible by 4.

The last two digits of 322A4828 are 28.

Since 28 ÷ 4 = 7 (Remainder = 0), the number is already divisible by 4.

The value of A (at the ten-thousands place) does not affect divisibility by 4.

The minimum possible digit that can be assigned to A is 0.

∴ The correct answer is 0.

Alternate Method

Given number: 322A4828

Divisibility Rule of 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This is because any number N can be written as (100 × k) + (last two digits), and 100 is always divisible by 4.

⇒ Number formed by last two digits = 28 ⇒ 28 ÷ 4 = 7 ⇒ Since the remainder is 0, the number 322A4828 is divisible by 4 for any digit value of A. ⇒ Possible values for A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ⇒ The question asks for the minimum value of A. ⇒ Minimum value = 0

∴ The correct answer is 0.

Additional Information

Divisibility by 8

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

Divisibility by 3 and 9

A number is divisible by 3 (or 9) if the sum of all its digits is divisible by 3 (or 9).

Divisibility by 11

The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Shortcut Trick

Speed of first lap (S₁) = 450 / 150 = 3 m/s.

Speed of second lap (S₂) = 450 / 75 = 6 m/s.

When distances are equal, Average Speed = (2 × S₁ × S₂) / (S₁ + S₂).

Average Speed = (2 × 3 × 6) / (3 + 6) = 36 / 9 = 4 m/s.

∴ The correct answer is 4.

Alternate Method

Given:

Distance of Lap 1 (D₁) = 450 m

Time for Lap 1 (T₁) = 150 sec

Distance of Lap 2 (D₂) = 450 m

Time for Lap 2 (T₂) = 75 sec

Formula Used:

Average Speed = Total Distance ÷ Total Time

⇒ Total Distance = D₁ + D₂ = 450 + 450 = 900 m

⇒ Total Time = T₁ + T₂ = 150 + 75 = 225 sec

⇒ Average Speed = 900 ÷ 225

⇒ Average Speed = 4 m/sec

∴ The correct answer is 4.

Additional Information

Average Speed (Equal Distances)

If a body travels two equal distances with speeds x and y, the average speed is given by (2xy) / (x + y).

Average Speed (Equal Time Intervals)

If a body travels for two equal time intervals with speeds x and y, the average speed is (x + y) / 2.

Unit Conversion

To convert speed from m/sec to km/hr, multiply the value by 18/5. To convert km/hr to m/sec, multiply by 5/18.

Shortcut Trick

Use the complementary angle identity: cos² θ + cos² (90° − θ) = 1.

Here, 30° + 60° = 90°, so cos² 30° + cos² 60° = 1.

The value of cos 90° is 0, so cos² 90° = 0.

Total sum = 1 + 0 = 1.

∴ The correct answer is 1.

Alternate Method

Given:

Expression = cos² 30° + cos² 60° + cos² 90°

Formula Used:

cos θ = Adjacent / Hypotenuse

Calculations:

⇒ cos 30° = √3 / 2

⇒ cos 60° = 1 / 2

⇒ cos 90° = 0

Substitute these values into the expression:

⇒ (√3 / 2)² + (1 / 2)² + (0)²

⇒ (3 / 4) + (1 / 4) + 0

⇒ 4 / 4

⇒ 1

∴ The correct answer is 1.

Additional Information

Trigonometric Identity

The fundamental identity states that sin²θ + cos²θ = 1 for any angle θ.

Complementary Angle Rule

For complementary angles A and B (where A + B = 90°), sin A = cos B and cos A = sin B.

Standard Cosine Values

Standard values include cos 0° = 1, cos 45° = 1/√2, and cos 90° = 0.

Shortcut Trick

Total Surface Area (TSA) = Curved Surface Area (CSA) + 2 × Base Area

Base Area = πr² = (22/7) × 14 × 14 = 616 m²

2 × Base Area = 2 × 616 = 1232 m²

CSA = TSA − 2 × Base Area = 3080 − 1232 = 1848 m²

∴ The correct answer is 1848 m².

Alternate Method

Given:

Total Surface Area (TSA) = 3080 m²

Radius (r) = 14 m

Formula Used:

TSA of cylinder = 2πr(h + r)

Curved Surface Area (CSA) of cylinder = 2πrh

Calculations:

⇒ 3080 = 2 × (22/7) × 14 × (h + 14)

⇒ 3080 = 2 × 22 × 2 × (h + 14)

⇒ 3080 = 88 × (h + 14)

⇒ h + 14 = 3080 ÷ 88

⇒ h + 14 = 35

⇒ h = 35 − 14 = 21 m

⇒ CSA = 2 × (22/7) × 14 × 21

⇒ CSA = 2 × 22 × 2 × 21

⇒ CSA = 88 × 21

⇒ CSA = 1848 m²

∴ The correct answer is 1848 m².

Additional Information

Volume of Cylinder

The space occupied by a cylinder is given by Volume = πr²h.

Hollow Cylinder

For a hollow cylinder with outer radius R and inner radius r, TSA = 2πh(R + r) + 2π(R² − r²).

Base Perimeter

The perimeter or circumference of the base of a cylinder is 2πr, which when multiplied by height gives the CSA.

Shortcut Trick

SP = (100 − Discount%)% of MP

SP = (100 − 12)% of 775

SP = 88% of 775 = 0.88 × 775

SP = 682

∴ The correct answer is ₹682.

Alternate Method

Given: Marked Price (MP) = ₹775 | Discount % = 12%

Formula: Selling Price (SP) = Marked Price − Discount

⇒ Discount amount = (Discount% / 100) × MP

⇒ Discount amount = (12 / 100) × 775

⇒ Discount amount = 0.12 × 775 = 93

⇒ SP = MP − Discount amount

⇒ SP = 775 − 93 = 682

∴ The correct answer is ₹682.

Additional Information

Discount Percentage

Discount % is always calculated on the Marked Price (MP) of an article: Discount % = (Discount / MP) × 100.

Successive Discounts

If two successive discounts of a% and b% are given, the net discount is [a + b − (a × b)/100]%.

Relationship between MP and CP

The ratio of Marked Price to Cost Price is given by MP/CP = (100 + Profit%)/(100 − Discount%).

Shortcut Trick

Rate 15% = 3/20 ⇒ Ratio of P : A for 1 year = 20 : 23

For 2 years, Ratio = 20² : 23² = 400 : 529

Given Principal 400 units = ₹6,400

1 unit = 6,400 ÷ 400 = 16

Amount = 529 units × 16 = ₹8,464

∴ The correct answer is ₹8,464.

Alternate Method

Given: Principal (P) = ₹6,400, Rate (R) = 15%, Time (n) = 2 years

Formula Used: Amount (A) = P(1 + R/100)ⁿ

⇒ A = 6400 × (1 + 15/100)²

⇒ A = 6400 × (115/100) × (115/100)

⇒ A = 6400 × (23/20) × (23/20)

⇒ A = 6400 × (529/400)

⇒ A = 16 × 529

⇒ A = 8464

∴ The correct answer is ₹8,464.

Additional Information

Effective Rate for Compound Interest

For 2 years, the effective rate of interest can be calculated as x + y + (x × y)/100. Here, 15 + 15 + (15 × 15)/100 = 32.25%.

Difference between CI and SI

The difference between CI and SI for 2 years is P(R/100)². In this case, 6400 × (15/100)² = ₹144.

Compound Interest Formula

The interest alone can be calculated using CI = P[(1 + R/100)ⁿ − 1].

Shortcut Trick

Ratio of Mother : Daughter (Present) = 2 : 1 (Difference = 1 unit)

Ratio of Mother : Daughter (10 yrs ago) = 3 : 1 (Difference = 2 units)

Make differences equal: Present Ratio = (2 : 1) × 2 = 4 : 2

Unit difference (4 → 3 or 2 → 1) is 1 unit = 10 years.

Mother's present age = 4 units = 4 × 10 = 40 years.

∴ The correct answer is 40 years.

Alternate Method

Given:

Present age Mother = 2 × Daughter's age

10 years ago Mother's age = 3 × (Daughter's age − 10)

Formula Used:

Linear Equation based on Age conditions.

Let the present age of the Daughter be x years.

⇒ Present age of the Mother = 2x years.

Age 10 years ago:

⇒ Daughter's age = (x − 10)

⇒ Mother's age = (2x − 10)

According to the condition:

⇒ (2x − 10) = 3 × (x − 10)

⇒ 2x − 10 = 3x − 30

⇒ 3x − 2x = 30 − 10

⇒ x = 20

Present age of the Mother:

⇒ Mother = 2x = 2 × 20

⇒ Mother = 40 years.

∴ The correct answer is 40 years.

Additional Information

Constant Age Difference

The difference between the ages of two persons remains constant throughout their lives. Always use this to balance ratios.

Ratio Balancing Method

If the age difference in units is not the same, multiply the ratios by the opposite difference values to make the gap equal.

Averages of Ages

If the average age of n people is A, after t years, the new average age will be (A + t).

Shortcut Trick

Remaining distance fraction = 1 − 2/3 = 1/3 of 228 km = 76 km

Remaining time fraction = 1 − 5/8 = 3/8 of 8 hours = 3 hours

Required speed = Remaining distance ÷ Remaining time

Speed = 76 ÷ 3 = 25.33... ≈ 25.3 km/hr

∴ The correct answer is 25.3.

Alternate Method

Given: Total Distance = 228 km, Total Time = 8 hours

Formula: Speed = Distance ÷ Time

⇒ Total Distance = 228 km

⇒ Distance covered = (2/3) × 228 = 152 km

⇒ Remaining Distance = 228 − 152 = 76 km

⇒ Total Time = 8 hours

⇒ Time spent = (5/8) × 8 = 5 hours

⇒ Remaining Time = 8 − 5 = 3 hours

⇒ Required Speed = 76 ÷ 3

⇒ Required Speed = 25.333...

∴ The correct answer is 25.3.

Additional Information

Average Speed

Average speed is defined as the Total Distance covered divided by the Total Time taken. Average Speed = Total Distance ÷ Total Time.

Unit Conversion

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

Constant Distance Relation

When distance is constant, speed is inversely proportional to time. S₁/S₂ = T₂/T₁.