Quantitative Aptitude PYQs

Shortcut Trick

Total Work (LCM of 10, 15, 30) = 30 units.

Efficiency: A = 3, B = 2, C = 1.

Work done by A in 2 days = 3 × 2 = 6 units.

Remaining work = 30 − 6 = 24 units.

Days taken by B and C = 24 ÷ (2 + 1) = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given:

Time taken by A = 10 days

Time taken by B = 15 days

Time taken by C = 30 days

Calculations:

⇒ Total Work = LCM(10, 15, 30) = 30 units.

⇒ Work done by A alone for 2 days = 3 × 2 = 6 units.

⇒ Remaining Work = Total Work − Work by A = 30 − 6 = 24 units.

⇒ Combined Efficiency of B and C = 2 + 1 = 3 units/day.

⇒ Time taken by B and C = Remaining Work ÷ Efficiency of (B + C)

⇒ Time taken = 24 ÷ 3 = 8 days.

∴ The correct answer is 8 days.

Additional Information

Total Work and Efficiency

Total Work = Efficiency × Time. Efficiency is inversely proportional to the time taken to complete the work.

Pipes and Cisterns

Similar to time and work, but inlet pipes have positive efficiency and outlet (leak) pipes have negative efficiency.

Work and Wages

Wages are generally distributed in the ratio of the work done by each individual, which is the product of efficiency and time worked.

Alternate Day Work

For work done on alternate days, calculate the work done in one complete cycle (e.g., 2 days or 3 days) and then find the total cycles required.

Shortcut Trick

Check for Pythagorean triplet: 15² + 20² = 225 + 400 = 625 = 25².

Since it is a right-angled triangle, the inradius (r) is given by the formula:

r = (Base + Perpendicular − Hypotenuse) ÷ 2

⇒ r = (15 + 20 − 25) ÷ 2

⇒ r = 10 ÷ 2 = 5 m.

∴ The correct answer is 5 m.

Alternate Method

Given: Sides of the triangular plot are a = 15 m, b = 20 m, and c = 25 m.

Formula Used:

1. Semi-perimeter (s) = (a + b + c) ÷ 2
2. Area (A) = √[s(s − a)(s − b)(s − c)]
3. Inradius (r) = Area ÷ Semi-perimeter

⇒ Semi-perimeter (s) = (15 + 20 + 25) ÷ 2 = 60 ÷ 2 = 30 m

⇒ Area (A) = √[30 × (30 − 15) × (30 − 20) × (30 − 25)]

⇒ Area (A) = √[30 × 15 × 10 × 5]

⇒ Area (A) = √[22500] = 150 m²

⇒ Inradius (r) = 150 ÷ 30

⇒ r = 5 m

∴ The correct answer is 5 m.

Additional Information

Inradius Property

For any triangle, the inradius is the ratio of the area of the triangle to its semi-perimeter (r = A/s).

Circumradius of Right Triangle

The circumradius (R) of a right-angled triangle is exactly half of the hypotenuse (R = c/2).

Right Triangle Inradius Shortcut

For a triangle with legs p, b and hypotenuse h, the inradius is r = (p + b − h) ÷ 2.

Shortcut Trick

Equate Volume to formula: (4/3) π r³ = 12π

Cancel π and solve for r³: r³ = (12 × 3) ÷ 4 = 9

Since 2³ = 8 and 3³ = 27, radius r = ³√9 ≈ 2.08 cm

∴ The correct answer is 2.08 cm.

Alternate Method

Given:

Volume of the Sphere (V) = 12π cm³

Formula Used:

Volume of a Sphere = (4/3) π r³

Calculations:

⇒ 12π = (4/3) × π × r³

⇒ 12 = (4/3) × r³

⇒ r³ = (12 × 3) ÷ 4

⇒ r³ = 3 × 3

⇒ r³ = 9

⇒ r = ³√9

⇒ r ≈ 2.08 cm

∴ The correct answer is 2.08 cm.

Additional Information

Surface Area of a Sphere

The total surface area is given by the formula 4πr².

Volume of a Hemisphere

A hemisphere is half of a sphere, and its volume is (2/3)πr³.

Surface Area of a Hemisphere

Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Relation between Radius and Volume

If the radius is doubled, the volume becomes 2³ = 8 times the original volume.

Shortcut Trick

For an equation 3A = 6B = 9C, the ratio A : B : C is the inverse of their coefficients.

Find the LCM of 3, 6, and 9, which is 18.

Divide the LCM by each coefficient: A = 18/3 = 6, B = 18/6 = 3, C = 18/9 = 2.

The resulting ratio is 6 : 3 : 2.

∴ The correct answer is 6 : 3 : 2.

Alternate Method

Given: 3A = 6B = 9C

Formula: If mA = nB = pC, then A : B : C = (1/m) : (1/n) : (1/p)

⇒ Let 3A = 6B = 9C = k

⇒ A = k/3, B = k/6, C = k/9

⇒ A : B : C = (k/3) : (k/6) : (k/9)

⇒ A : B : C = 1/3 : 1/6 : 1/9

⇒ Multiply by LCM(3, 6, 9) = 18 to remove fractions:

⇒ A : B : C = (1/3 × 18) : (1/6 × 18) : (1/9 × 18)

⇒ A : B : C = 6 : 3 : 2

∴ The correct answer is 6 : 3 : 2.

Additional Information

Inverse Proportion

When values are equated like mA = nB, the variables are in inverse proportion to their coefficients, meaning A/B = n/m.

Ratio Scaling

A ratio remains unchanged if all its terms are multiplied or divided by the same non-zero constant (like the LCM used above).

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd), used when multiple proportionalities interact.

Shortcut Trick

Speed of runner = 450 ÷ 90 = 5 m/s.

Speed of cyclist = 5 × 150% = 7.5 m/s.

Required time = 180 ÷ 7.5 = 24 sec.

∴ The correct answer is 24 sec.

Alternate Method

Given:

Distance covered by runner = 450 m

Time taken by runner = 90 sec

Distance to be covered by cyclist = 180 m

Formula Used:

Speed = Distance ÷ Time

Time = Distance ÷ Speed

Calculations:

⇒ Speed of the runner = 450 ÷ 90 = 5 m/s

⇒ Speed of the cyclist = 150% of 5 = (150/100) × 5

⇒ Speed of the cyclist = 1.5 × 5 = 7.5 m/s

⇒ Time taken by the cyclist for 180 m = 180 ÷ 7.5

⇒ Time = 1800 ÷ 75 = 24 sec

∴ The correct answer is 24 sec.

Additional Information

Unit Conversion

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

Relative Speed

When two objects move in the same direction, relative speed is (S₁ − S₂). In opposite directions, it is (S₁ + S₂).

Average Speed

Average speed = (Total Distance) ÷ (Total Time). For two equal distances at speeds x and y, it is 2xy ÷ (x + y).

Shortcut Trick

The average of 4 scores is 10, so the net deviation from this average must be zero.

Deviations of the three known scores: (6 − 10) = −4; (9 − 10) = −1; (11 − 10) = +1.

Sum of these deviations = −4 − 1 + 1 = −4.

To balance this, the fourth score must have a deviation of +4.

Fourth score = 10 + 4 = 14.

∴ The correct answer is 14.

Alternate Method

Given: Average = 10, Total observations (n) = 4, Known scores = 6, 9, 11.

Formula Used: Total Sum = Average × Number of observations

⇒ Total sum of 4 scores = 10 × 4 = 40

⇒ Sum of three known scores = 6 + 9 + 11 = 26

⇒ Let the fourth score be x.

⇒ 26 + x = 40

⇒ x = 40 − 26

⇒ x = 14

∴ The correct answer is 14.

Additional Information

Properties of Averages

If every observation is increased or decreased by a constant k, the new average also increases or decreases by k.

Weighted Average

The combined average of two groups is given by (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n and x represent size and average respectively.

Net Deviation Rule

The sum of deviations of all observations from their arithmetic mean is always equal to zero.

Shortcut Trick

The Selling Price (SP) is calculated by subtracting the Discount from the Marked Price (MP).

Direct Calculation: SP = 50 − 5 = 45.

∴ The correct answer is ₹45.

Alternate Method

Given:

⇒ Marked Price (MP) of the notebook = ₹50

⇒ Flat Discount allowed = ₹5

Formula Used:

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

Calculations:

⇒ Selling Price = 50 − 5

⇒ Selling Price = 45

The shopkeeper sells the notebook for ₹45 after reducing the marked price by the discount amount.

∴ The correct answer is ₹45.

Additional Information

Discount Percentage

It is the discount expressed as a percentage of the Marked Price: Discount % = (Discount ÷ MP) × 100.

Marked Price (MP)

Also known as the List Price or Tag Price, it is the price printed on the item before any discounts are applied.

Successive Discounts

When two or more discounts are given one after another, the net discount is calculated on the reducing balance or using the formula: a + b − (ab ÷ 100).

Shortcut Trick

Direct formula for the difference between Circumference and Diameter: 2r(π − 1) = Difference.

2r(22/7 − 1) = 44 ⇒ 2r(15/7) = 44.

r = (44 × 7) / 30 = 308 / 30 ≈ 10.27 cm.

Rounding to the nearest option, we get 10 cm.

∴ The correct answer is ≈ 10 cm.

Alternate Method

Given:

Difference between Circumference and Diameter = 44 cm

Value of π = 22/7

Formula Used:

Circumference of a circle = 2πr

Diameter of a circle = 2r

Calculations:

⇒ Circumference − Diameter = 44

⇒ 2πr − 2r = 44

⇒ 2r(π − 1) = 44

⇒ 2r(22/7 − 1) = 44

⇒ 2r((22 − 7) / 7) = 44

⇒ 2r(15/7) = 44

⇒ 30r / 7 = 44

⇒ 30r = 44 × 7

⇒ 30r = 308

⇒ r = 308 / 30

⇒ r = 10.266... cm

⇒ r ≈ 10.27 cm

Rounding to the nearest integer as per the options provided, the Radius is approximately 10 cm.

∴ The correct answer is ≈ 10 cm.

Additional Information

Area of a Circle

The total space enclosed within the boundary of a circle is called its Area, calculated as A = πr².

Relationship between C and D

The ratio of the Circumference to the Diameter of any circle is always a constant called π (π = C/D).

Semi-Circle Perimeter

The perimeter of a semi-circle is not just half the circumference, but includes the diameter: Perimeter = πr + 2r.

Shortcut Trick

If the discount is 30%, the Selling Price (SP) is simply 70% of the Marked Price (MP).

SP = (100 − 30)% of 900

SP = 70% × 900 = 0.7 × 900

SP = 630

∴ The correct answer is ₹630.

Alternate Method

Given:

Marked Price (MP) = ₹900

Discount Percentage = 30%

Formula Used:

Discount Amount = (Discount% ÷ 100) × Marked Price

Selling Price (SP) = Marked Price − Discount Amount

Calculations:

⇒ Discount Amount = (30 ÷ 100) × 900

⇒ Discount Amount = 0.3 × 900 = ₹270

⇒ Selling Price (SP) = 900 − 270

⇒ SP = ₹630

∴ The correct answer is ₹630.

Additional Information

Marked Price and Selling Price

Marked Price (MP) is the price printed on an item. The Selling Price (SP) is the actual amount after deducting the discount from the MP.

Discount Percentage Formula

Discount % = (Discount ÷ Marked Price) × 100. Always remember that discount is calculated on the Marked Price.

Successive Discounts

If two discounts d₁% and d₂% are given, the Equivalent Discount = [d₁ + d₂ − (d₁ × d₂)/100]%.

Shortcut Trick

The relationship between Speed, Time, and Distance is direct.

Distance = Speed × Time

Distance = 12 km/h × 5 hr = 60 km

∴ The correct answer is 60 km.

Alternate Method

Given:

Average Speed of the cycle = 12 km/h

Total Time spent cycling = 5 hr

Formula Used:

Total Distance = Average Speed × Total Time

Calculations:

⇒ Distance = 12 × 5

⇒ Distance = 60 km

∴ The correct answer is 60 km.

Additional Information

Basic Distance Formula

The distance traveled is the product of speed and time: D = S × T. Similarly, Speed = D/T and Time = D/S.

Unit Conversion

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

Average Speed

Average speed is defined as the Total Distance divided by the Total Time taken for the entire journey.

Shortcut Trick

Increase = 450 − 400 = 50.

Ratio of Increase to Original = 50 / 400 = 1 / 8.

Since 1 / 8 is equivalent to 12.5%, the percentage increase is 12.5%.

∴ The correct answer is 12.5%.

Alternate Method

Given:

Initial marks = 400

Final marks = 450

Formula Used:

Percentage Increase = [(New Value − Old Value) / Old Value] × 100

Calculations:

⇒ Actual Increase = 450 − 400 = 50

⇒ Percentage Increase = (50 / 400) × 100

⇒ Percentage Increase = (1 / 8) × 100

⇒ Percentage Increase = 12.5%

∴ The correct answer is 12.5%.

Additional Information

Percentage Change Formula

The percentage change is calculated as (Change / Original Value) × 100. It is positive for an increase and negative for a decrease.

Common Fractional Conversions

Memorizing common fractions helps in speed: 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/10 = 10%, 1/12 = 8.33%.

Base Value Importance

Always ensure the Initial Value (the value before the change) is used in the denominator when calculating percentage growth.

Shortcut Trick

Ratio of Profit to Cost Price = 120 : 600

⇒ Profit : CP = 1 : 5

Fractional conversion: 1/5 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Cost Price (CP) = ₹600

Profit = ₹120

Formula Used:

Profit Percentage = (Profit ÷ Cost Price) × 100

Calculations:

⇒ Profit % = (120 ÷ 600) × 100

⇒ Profit % = (1 ÷ 5) × 100

⇒ Profit % = 20%

∴ The correct answer is 20%.

Additional Information

Selling Price Formula

Selling Price (SP) can be calculated as CP + Profit or CP − Loss.

Loss Percentage

Loss % = (Loss ÷ CP) × 100. Note that both profit and loss are always calculated on the Cost Price (CP) unless stated otherwise.

Profit in terms of SP and CP

Profit = SP − CP. If SP > CP, the trader makes a profit; if CP > SP, the trader incurs a loss.

Shortcut Trick

Speed of Car = 180 ÷ 3 = 60 km/h.

Given Speed Ratio (Car : Bus) = 3 : 2.

Since 3 units = 60 km/h, then 1 unit = 20 km/h.

Bus Speed = 2 units = 40 km/h.

Distance covered by Bus in 2 hr = 40 × 2 = 80 km.

∴ The correct answer is 80 km.

Alternate Method

Given:

Speed Ratio (Car : Bus) = 3 : 2

Distance (Car) = 180 km, Time (Car) = 3 hr

Time (Bus) = 2 hr

Formula Used:

Speed = Distance ÷ Time

Distance = Speed × Time

Calculations:

⇒ Speed of Car = 180 ÷ 3

⇒ Speed of Car = 60 km/h

⇒ According to ratio, 3x = 60

⇒ x = 20

⇒ Speed of Bus = 2x = 2 × 20 = 40 km/h

⇒ Distance covered by Bus = Speed_Bus × Time

⇒ Distance = 40 × 2

⇒ Distance = 80 km

∴ The correct answer is 80 km.

Additional Information

Speed-Distance Relation

When Time is constant, Distance is directly proportional to Speed (D₁/D₂ = S₁/S₂).

Unit Conversion

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

Average Speed

If a body travels two equal distances at speeds x and y, the Average Speed = 2xy / (x + y).

Shortcut Trick

Distance in meters = 2.7 × 1000 = 2700 m

Time = Total Distance ÷ Speed

Time = 2700 ÷ 90 = 30 min

∴ The correct answer is 30 min.

Alternate Method

Given:

Speed of the person = 90 m/min

Total Distance to walk = 2.7 km

Formula Used:

Time = Distance ÷ Speed

Calculations:

⇒ Distance = 2.7 × 1000 meters

⇒ Distance = 2700 m

⇒ Time = 2700 ÷ 90

⇒ Time = 30 minutes

∴ The correct answer is 30 min.

Additional Information

Unit Conversion

To convert kilometers to meters, multiply by 1000 (1 km = 1000 m). To convert hours to minutes, multiply by 60.

Speed-Distance-Time Triangle

The core relationship is Distance = Speed × Time. From this, Speed = Distance ÷ Time and Time = Distance ÷ Speed.

Speed Unit Conversion

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

Shortcut Trick

Product of ratio parts: 2 × 3 = 6 units².

Area calculation: 6 units² = 150 ⇒ 1 unit² = 25 ⇒ 1 unit = 5 cm.

Rectangle sides: 2 × 5 = 10 cm and 3 × 5 = 15 cm.

Triangle sides: 10, √150 = 5√6, and 15 ÷ 2 = 7.5.

Perimeter: 10 + 7.5 + 5√6 = 17.5 + 5√6 cm.

∴ The correct answer is 17.5 + 5√6 cm.

Alternate Method

Given: Area = 150 cm², Side Ratio = 2 : 3.

Formula Used: Area of Rectangle = Length × Breadth; Perimeter of Triangle = Sum of all sides.

Let the sides of the rectangle be 2x and 3x.

⇒ Area = 2x × 3x = 6x²

⇒ 6x² = 150

⇒ x² = 25 ⇒ x = 5 cm

⇒ Smaller side = 2 × 5 = 10 cm

⇒ Larger side = 3 × 5 = 15 cm

Triangle sides construction:

⇒ Side 1 = Smaller side = 10 cm

⇒ Side 2 = Square root of area = √150 = √(25 × 6) = 5√6 cm

⇒ Side 3 = Half of larger side = 15 ÷ 2 = 7.5 cm

⇒ Perimeter of the triangle = 10 + 5√6 + 7.5

⇒ Perimeter = 17.5 + 5√6 cm

∴ The correct answer is 17.5 + 5√6 cm.

Additional Information

Perimeter of a Rectangle

The total distance around the rectangle is given by 2 × (Length + Breadth).

Heron's Formula for Triangle Area

For a triangle with sides a, b, and c, Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2.

Relationship between Square and Rectangle

For a given perimeter, a square has a larger area than any other rectangle.

Pythagorean Triplets

If a triangle is right-angled, its sides satisfy a² + b² = c², such as 3-4-5 or 5-12-13.

Shortcut Trick

The Area of a square can be directly calculated from its diagonal using the formula: Area = (Diagonal²) ÷ 2.

Given Diagonal = 10√2 cm.

Area = (10√2)² ÷ 2

Area = (100 × 2) ÷ 2 = 100 cm².

∴ The correct answer is 100 cm².

Alternate Method

Given:

⇒ Diagonal of the square = 10√2 cm

Formula Used:

⇒ Diagonal of a square = Side × √2

⇒ Area of a square = Side²

Calculations:

⇒ 10√2 = Side × √2

⇒ Side (s) = 10 cm

⇒ Area = (10 cm)²

⇒ Area = 100 cm²

⇒ Thus, the result matches Option (2).

∴ The correct answer is 100 cm².

Additional Information

Perimeter of a Square

The total boundary length of a square is given by the formula Perimeter = 4 × side.

Diagonal Property

The diagonal of a square is the longest line segment connecting two opposite vertices, equal to s√2.

Area in terms of Diagonal

The Area can also be expressed as (d²)/2, which is useful when the side length is not directly known.

Shortcut Trick

Ratio of sides = 3 : 3 : 2 (since the triangle is isosceles).

Total perimeter units = 3 + 3 + 2 = 8 units.

8 units = 32 cm ⇒ 1 unit = 4 cm.

Sides are 12 cm, 12 cm and base is 8 cm.

Area = (Base/4) × √(4×Side² − Base²) = (8/4) × √(4×144 − 64) = 2 × √512 ≈ 45.25 cm².

∴ The correct answer is 45.25 cm².

Alternate Method

Given: Perimeter of triangle = 32 cm, Ratio of equal sides to base = 3 : 2.

Formula Used: Area = 1/2 × Base × Height; Height (h) = √(Side² − (Base/2)²).

⇒ Let the equal sides be 3x and the base be 2x.

⇒ Perimeter = 3x + 3x + 2x = 8x.

⇒ 8x = 32 ⇒ x = 4.

⇒ Equal sides (a) = 3 × 4 = 12 cm; Base (b) = 2 × 4 = 8 cm.

⇒ Height (h) = √(12² − (8/2)²) = √(144 − 16) = √128 = 8√2 cm.

⇒ Area = 1/2 × 8 × 8√2 = 32 × 1.4142 ≈ 45.2544 cm².

∴ The correct answer is 45.25 cm².

Additional Information

Heron's Formula

Used to find the area of any triangle when all sides (a, b, c) are known: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2.

Isosceles Triangle Properties

An isosceles triangle has two equal sides and two equal base angles. The altitude from the vertex bisects the base at a right angle.

Area of Isosceles Triangle

The specific formula for the area is (b/4) × √(4a² − b²), where 'a' is the length of equal sides and 'b' is the base.

Shortcut Trick

Total work (LCM of 12, 18, 24) = 72 units.

Efficiencies: A = 6, B = 4, C = 3 (Total = 13 units/day).

Work done in first 4 days = 13 × 4 = 52 units.

Remaining work = 72 − 52 = 20 units.

Additional days for A and B = 20 ÷ (6 + 4) = 2 days.

∴ The correct answer is 2 days.

Alternate Method

Given: A takes 12 days, B takes 18 days, and C takes 24 days. C leaves after 4 days.

Formula: Total Work = Efficiency × Time

Calculations:

⇒ Total efficiency of A + B + C = 6 + 4 + 3 = 13 units/day

⇒ Work completed in 4 days = 13 × 4 = 52 units

⇒ Remaining work = Total work − Completed work = 72 − 52 = 20 units

⇒ Efficiency of A + B = 6 + 4 = 10 units/day

⇒ Additional days required = Remaining work ÷ (Efficiency of A + B)

⇒ Additional days = 20 ÷ 10 = 2 days

∴ The correct answer is 2 days.

Additional Information

Pipes and Cisterns

Similar to Time and Work, but inlet pipes have positive efficiency and outlet (leakage) pipes have negative efficiency.

Work and Wages

Wages are always distributed in the ratio of the actual work done or the efficiency ratio (if time is same).

Alternate Day Work

Calculate the total work done in one complete cycle (e.g., 2 days or 3 days) and then find the nearest multiple to the total work.

Shortcut Trick

To find the Ratio P : Q : R from 8P = 4Q = 2R, find the LCM of coefficients (8, 4, 2).

LCM of 8, 4, and 2 is 8.

Divide the LCM by each coefficient: P = 8/8, Q = 8/4, R = 8/2.

P : Q : R = 1 : 2 : 4.

∴ The correct answer is 1 : 2 : 4.

Alternate Method

Given: 8P = 4Q = 2R

Formula Used: If aP = bQ = cR, then P : Q : R = (1/a) : (1/b) : (1/c)

Let 8P = 4Q = 2R = k (where k is a constant)

⇒ 8P = k → P = k/8

⇒ 4Q = k → Q = k/4

⇒ 2R = k → R = k/2

⇒ P : Q : R = (k/8) : (k/4) : (k/2)

⇒ P : Q : R = 1/8 : 1/4 : 1/2

⇒ To remove fractions, multiply by the LCM of denominators (8, 4, 2) which is 8:

⇒ P : Q : R = (1/8 × 8) : (1/4 × 8) : (1/2 × 8)

⇒ P : Q : R = 1 : 2 : 4

∴ The correct answer is 1 : 2 : 4.

Additional Information

Inverse Proportion in Ratios

When terms are related by multiplication (aP = bQ), their Ratio is the Inverse of their coefficients. Larger coefficients result in smaller ratio parts.

Ratio Simplification Rule

A Ratio remains unchanged if all its terms are multiplied or divided by the same non-zero quantity.

Continued Proportion

If P/Q = Q/R, then P, Q, and R are in Continued Proportion, and Q² = P × R.

Shortcut Trick

Speed of bicycle = 180 ÷ 15 = 12 km/hr

Speed of moped = 250% of 12 = 12 × 2.5 = 30 km/hr

Distance covered by moped in 2.5 hr = 30 × 2.5 = 75 km

∴ The correct answer is 75 km.

Alternate Method

Given:

Distance covered by bicycle = 180 km

Time taken by bicycle = 15 hr

Ratio of speed of moped to bicycle = 250 : 100 = 2.5 : 1

Time taken by moped = 2¹/₂ hr = 2.5 hr

Formula Used:

Speed = Distance ÷ Time

Distance = Speed × Time

Calculations:

⇒ Bicycle Speed = 180 ÷ 15 = 12 km/hr

⇒ Moped Speed = (250 ÷ 100) × 12

⇒ Moped Speed = 2.5 × 12 = 30 km/hr

⇒ Distance covered by moped = 30 km/hr × 2.5 hr

⇒ Distance = 75 km

∴ The correct answer is 75 km.

Additional Information

Speed, Distance, and Time Relation

The fundamental relation is Distance = Speed × Time. If speed is constant, distance is directly proportional to time.

Unit Conversion

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

Percentage Change in Speed

If speed increases by x%, the new speed is Initial Speed × (100 + x)/100. Here, 250% of the speed means a 150% increase.