Question 1

Suresh started cycling along the boundaries of a square field from corner point A. After half an hour, he reached the corner point C, diagonally opposite to A, if his speed was 8km/hr , what is the area of the field in square km.?

Accepted Answer

Length of two sides of square = 8 x 1/2 km. = 4 km. ∴ Area of the field = 2 x 2 sq. km = 4 sq. km.

Question 2

A man goes uphill with an average speed of 35 km/hr, and covers down with an average speed of 45 km/hr. The distance travelled in both the cases being the same , the average speed for the entire journey is?

Accepted Answer

Average speed = 2uv / (u + v) = ( 2 x 35 x 45) / (35 + 45) km/hr. = 39 3/8 km/hr

Question 3

If a boy takes as much time in running 10 m as a car takes in covering 25 m, the distance covered by the boy during the time the car covers 1 km, is?

Accepted Answer

Let distance covered by boy is Y. Then, 25 : 10 : : 1000 : Y ⇒ Y = (10 x 1000)/25 = 400 m

Question 4

The ratio between the rates of walking of A and B is 2:3 , if the time taken by B to cover a certain distance is 36 minutes, the time taken by A to cover that much distance is?

Accepted Answer

Ratio of speed = 2 : 3 Ratio of times taken for same distance = 1/2 : 1/3 From question 1/2 : 1/3 = t : 36 ⇒ (1/3) x t = (1/2) x 36 ∴ x = 54 min .

Question 5

A man, on tour travel first 160 km. at 64 km/hr. and the next 160 km. at 80 km/hr. The average speed for first 320 km. of the tour is?

Accepted Answer

Average speed = 2uv / ( u + v ) km/hr =(2 x 64 x 80) / (64 + 80) km/hr = (2 x 64 x 80) / 144 km/hr. = 71.11 km/hr

Question 6

By walking at 3/4 of his usual speed , a man reaches his office 20 minutes later than usual . this usual time is?

Accepted Answer

At 3/4 of the usual speed, the time taken is 4/3 of the usual time ∴ 4/3 of usual time - usual time = 20 min ⇒ 4x/3 - x = 20 ⇒ x/3 = 20 ∴ x = 60 min.

Question 7

A train is running with the speed of 45 km/hour. What is its speed in meter per second?

Accepted Answer

speed of a train in kilometer per hour =45 Speed in meter per second = ( 5/18 ) x Speed in kilometer per hour = 45 x 5/18 = 12.5 kmph

Question 8

If a motor car covers a distance of 250 m in 25 second, What is its speed in kilometer per hour?

Accepted Answer

Speed of the motor car in meter per second = 250 / 25 = 10 m/s Speed in km/hr = (18/5) x speed in m/s = 10 x (18 / 5) km/hour =36 km/hour.

Question 9

A man takes 4 h 20 min in walking to a certain place and riding back. If he walk on both sides he losses 1 h. The time he would take by riding both ways is?

Accepted Answer

W + R = 4 h 20 min W + W = 5 h 20 min ∴ R + R = 3 h 20 min

Question 10

A boat covers 1 km downstream in 5 minutes and 1 km upstream in 12 minutes. What is the speed of the current (in km/h)?

Accepted Answer

Introduction / Context: River-boat problems compare downstream (with current) and upstream (against current) speeds. The still-water speed and the current's speed can be recovered from these two observed speeds using simple averages and differences. Given Data / Assumptions: Downstream: 1 km in 5 minutes. Upstream: 1 km in 12 minutes. Speeds are constant; current is uniform. Concept / Approach: If v_b is boat speed in still water and v_c is current speed, then downstream speed v_d = v_b + v_c and upstream speed v_u = v_b − v_c. Hence v_b = (v_d + v_u)/2 and v_c = (v_d − v_u)/2. Step-by-Step Solution: Convert times to hours: 5 min = 5/60 h; 12 min = 12/60 h.v_d = distance / time = 1 / (5/60) = 12 km/h.v_u = 1 / (12/60) = 5 km/h.Current speed v_c = (v_d − v_u) / 2 = (12 − 5)/2 = 3.5 km/h. Verification / Alternative check: Boat's still-water speed v_b = (12 + 5)/2 = 8.5 km/h. Check: 8.5 + 3.5 = 12 (downstream), 8.5 − 3.5 = 5 (upstream), which matches the given data. Why Other Options Are Wrong: 4.5 km/h or 2.5 km/h assume incorrect averaging; 2 km/h is too small given a large downstream advantage. Common Pitfalls: Using arithmetic mean for the current or mixing minutes with hours without converting units consistently. Final Answer: 3.5 km/h

Question 11

A person travels from home to office at 4 km/h and returns at 6 km/h over the same route. What is the average speed for the entire trip?

Accepted Answer

Introduction / Context: Average speed over equal distances at two different speeds is not the arithmetic mean; it is the harmonic mean. This scenario appears whenever you go and return over the same path but at different speeds. Given Data / Assumptions: Outbound speed = 4 km/h. Return speed = 6 km/h. Distances out and back are equal. Concept / Approach: For equal distances with speeds u and v, average speed v_avg = 2uv / (u + v). This comes from total distance divided by total time, with time = distance/speed for each leg. Step-by-Step Solution: Let each leg be distance d. Total distance = 2d.Total time = d/4 + d/6 = (3d + 2d)/12 = 5d/12 hours.Average speed = total distance / total time = 2d / (5d/12) = 24/5 = 4.8 km/h. Verification / Alternative check: Harmonic mean formula gives v_avg = 2*4*6/(4+6) = 48/10 = 4.8 km/h, confirming the calculation. Why Other Options Are Wrong: 4.5 and 5 km/h are near but incorrect; 10 km/h is impossible as it exceeds both segment speeds. Common Pitfalls: Using the arithmetic mean (which would be 5 km/h) instead of the harmonic mean for equal distances. Final Answer: 4.8 km/h

Question 12

A traveler covers three equal legs of 39 km each at 26 km/h, 39 km/h, and 52 km/h respectively. What is the average speed for the entire 117 km journey?

Accepted Answer

Introduction / Context: When multiple legs cover equal distances at different speeds, the overall average speed must be computed from total distance divided by total time; it is not the simple average of the speeds. Given Data / Assumptions: Leg distances: 39 km each (total 117 km). Speeds: 26 km/h, 39 km/h, 52 km/h. Constant speeds per leg; negligible stops. Concept / Approach: Total time is the sum of leg times: t = 39/26 + 39/39 + 39/52 hours. Average speed = total distance / total time. Step-by-Step Solution: Compute times: 39/26 = 1.5 h; 39/39 = 1 h; 39/52 = 0.75 h.Total time = 1.5 + 1 + 0.75 = 3.25 h.Total distance = 39 + 39 + 39 = 117 km.Average speed = 117 / 3.25 = 36 km/h. Verification / Alternative check: Multiply 36 km/h by 3.25 h: 36*3 = 108; 36*0.25 = 9; total 117 km, matching the distance. Why Other Options Are Wrong: 33 and 34 km/h underestimate the pace; 38 km/h is too high given the time spent at 26 km/h on one full leg. Common Pitfalls: Averaging the three speeds arithmetically, which ignores varying times per leg. Final Answer: 36 km/h

Question 13

Convert the speed 3 1/3 m/s into kilometers per hour (km/h).

Accepted Answer

Introduction / Context: Unit conversions between meters per second (m/s) and kilometers per hour (km/h) are standard. The fixed multiplier simplifies such conversions once memorized. Given Data / Assumptions: Speed = 3 1/3 m/s = 10/3 m/s. Conversion factor: 1 m/s = 18/5 km/h. Concept / Approach: To convert m/s to km/h, multiply by 18/5. This follows from 1 m = 0.001 km and 1 s = 1/3600 h, so (m/s) * (3600/1000) = (18/5) km/h. Step-by-Step Solution: Express speed as an improper fraction: 3 1/3 = 10/3 m/s.Multiply by 18/5: (10/3)*(18/5) = 180/15 = 12 km/h. Verification / Alternative check: Reverse conversion: 12 km/h to m/s = 12*(5/18) = 10/3 m/s, confirming consistency. Why Other Options Are Wrong: 8, 9, and 10 km/h are below the exact converted value; only 12 km/h matches. Common Pitfalls: Using 5/18 instead of 18/5 when converting from m/s to km/h. Final Answer: 12 km/h

Question 14

A car covers 300 km in 15 hours. What is the speed of the car (in km/h)?

Accepted Answer

Introduction / Context: The fundamental speed relation is speed = distance / time. This direct application checks comfort with basic units and arithmetic. Given Data / Assumptions: Distance = 300 km. Time = 15 h. Uniform speed throughout. Concept / Approach: Apply speed = distance / time and simplify. Step-by-Step Solution: Speed = 300 / 15 = 20 km/h. Verification / Alternative check: At 20 km/h for 15 h, distance = 20*15 = 300 km, which matches the given distance. Why Other Options Are Wrong: 25, 24, and 15 km/h do not satisfy 300 = speed * 15 given exact integers. Common Pitfalls: Accidentally converting units (e.g., to minutes) without need; overcomplicating a straightforward division. Final Answer: 20 km/h

Question 15

A car travels 690 km in 30 hours. What is its average speed (in km/h)?

Accepted Answer

Introduction / Context: Average speed over a single uninterrupted leg equals distance divided by total time. Here, the numbers are chosen for a clean division. Given Data / Assumptions: Distance = 690 km. Time = 30 h. Concept / Approach: Average speed = distance / time. Step-by-Step Solution: Average speed = 690 / 30 = 23 km/h. Verification / Alternative check: 23 km/h * 30 h = 690 km, reconciling with the given distance. Why Other Options Are Wrong: 25, 20, 18 km/h yield 750, 600, 540 km respectively over 30 h, not 690 km. Common Pitfalls: Mistyping the division or rounding unnecessarily when the quotient is exact. Final Answer: 23 km/h

Question 16

A bus runs uniformly at 37 km/h. How far does it travel in 8 hours?

Accepted Answer

Introduction / Context: Distance is the product of speed and time for motion at uniform speed. This checks direct application with tidy integers. Given Data / Assumptions: Speed = 37 km/h. Time = 8 h. Uniform motion; no stops. Concept / Approach: Distance = speed * time. Step-by-Step Solution: Distance = 37 * 8 = 296 km. Verification / Alternative check: Reverse: 296 km / 8 h = 37 km/h, the given speed. Why Other Options Are Wrong: 246, 289, and 276 km correspond to 30.75, 36.125, and 34.5 km/h over 8 h, not 37 km/h. Common Pitfalls: Arithmetic slips in multiplication. Final Answer: 296 km

Question 17

A bus covers 400 km at 20 km/h. How much time does it take to cover this distance?

Accepted Answer

Introduction / Context: Time is distance divided by speed for uniform motion. The numbers lead to an exact integer solution. Given Data / Assumptions: Distance = 400 km. Speed = 20 km/h. Concept / Approach: Use time = distance / speed. Step-by-Step Solution: Time = 400 / 20 = 20 h. Verification / Alternative check: Check: 20 km/h for 20 h yields 400 km. Why Other Options Are Wrong: 25 h would imply 16 km/h; 5 h implies 80 km/h; 21 h implies ~19.05 km/h, none matching 20 km/h. Common Pitfalls: Inverting the ratio and mistakenly multiplying speed by time instead of dividing distance by speed when solving for time. Final Answer: 20 h

Question 18

A bus moves at 72 km/h. What distance (in meters) does it cover in 5 seconds?

Accepted Answer

Introduction / Context: This problem combines a unit conversion (km/h to m/s) with a time-based distance calculation. It reinforces correct use of the 5/18 factor and proportional reasoning over seconds. Given Data / Assumptions: Speed = 72 km/h. Time = 5 s. Concept / Approach: Convert speed to m/s: v(m/s) = v(km/h) * 5/18. Then distance = speed * time in consistent units. Step-by-Step Solution: Convert speed: 72 * (5/18) = 4 * 5 = 20 m/s.Distance in 5 s = 20 * 5 = 100 m. Verification / Alternative check: Back-convert: 100 m in 5 s implies 20 m/s = 72 km/h, confirming consistency. Why Other Options Are Wrong: 50 m corresponds to 10 m/s (36 km/h); 60 m corresponds to 12 m/s (43.2 km/h); 74.5 m is a non-integer artifact not supported by exact conversion. Common Pitfalls: Using 18/5 instead of 5/18 when converting from km/h to m/s; mixing seconds with hours without converting. Final Answer: 100 m

Question 19

Ram and Shyam walk towards each other on a straight line with speeds of 10 km/h and 6 km/h. What is Ram’s speed relative to Shyam?

Accepted Answer

Introduction / Context: Relative speed quantifies how fast one moving object approaches or recedes from another. When two bodies move in opposite directions along the same line, their relative speed is the sum of their individual speeds. Given Data / Assumptions: Speed of Ram = 10 km/h. Speed of Shyam = 6 km/h. They move directly towards each other (opposite directions). Concept / Approach: Relative speed (opposite directions) = u + v. This arises because, in a time interval, the distance between them shrinks by the amount each covers towards the other. Step-by-Step Solution: u = 10 km/h, v = 6 km/h.Relative speed = u + v = 10 + 6 = 16 km/h. Verification / Alternative check: If they start 16 km apart, at the computed relative speed they meet in 1 hour; Ram covers 10 km and Shyam 6 km, consistent with their speeds. Why Other Options Are Wrong: 6, 4, and 8 km/h are sums/differences not appropriate for opposite-direction motion; only 16 km/h matches the add rule. Common Pitfalls: Using the difference of speeds (which applies to same-direction chasing), not the sum used for opposite directions. Final Answer: 16 km/h

Question 20

Relative speed (same direction) Two cars travel in the same direction at 9 km/h and 5 km/h. What is the speed of the first car relative to the second?

Accepted Answer

Introduction / Context: Relative speed measures how fast one object approaches or recedes from another. For motion along a straight line in the same direction, the relative speed equals the difference of their individual speeds (faster minus slower). Given Data / Assumptions: First car speed = 9 km/h. Second car speed = 5 km/h. Both move in the same direction on a straight path with constant speeds. Concept / Approach: For same-direction motion, relative speed = |v1 − v2|. We take the faster car's speed minus the slower car's speed to obtain the rate at which the gap changes. Step-by-Step Solution: Relative speed = 9 − 5 = 4 km/h Verification / Alternative check: If you imagine sitting in the slower car, the faster car appears to move past you at 4 km/h. Conversely, from the faster car, the slower one seems to drift backward at 4 km/h. Why Other Options Are Wrong: 2 km/h and 6 km/h correspond to wrong differences. 8 km/h is the sum, which applies to opposite directions, not the same direction. Common Pitfalls: Using the sum 9 + 5 for same-direction cases; the sum only applies when objects move toward each other. Final Answer: 4 km/h

Time and Distance Questions