Trial Test 2 : Work : Speed : Distance : Time

Work : Speed : Distance : Time


Main Formulas



  • Speed = Distance ÷ Time (v = d/t)

  • Distance = Speed × Time ( d = v × t)

  • Time = Distance ÷ Speed ( t = d/v)

  • Time & Work Formula = M × D × H ∝ Work 


Where:



  • M = Men

  • D = Days

  • H = Hours

  • Work = Total work done / Output


Main Rule


If the work is constant → M × D × H = Constant


i. Men & Days Relation


If hours/day are the same: M1⋅D1=M2⋅D2



  • More men → work finishes faster

  • Fewer men → work takes longer


ii. Men & Hours Relation


If the number of days is the same: M1⋅H1=M2⋅H2


iii. Days & Hours Relation


If the number of men is the same: D1⋅H1=D2⋅H2


 


1. A, B, and C can complete a work in 10, 12, and 15 days respectively. If all three work together, in how many days will the work be completed ?


Soln:


Work rates per day:



  • A = 1/10 per day

  • B = 1/12 per day

  • C = 1/15 per day


Combined work per day:


= 1/10+1/12+1/15


= (6+5+4)/60


= 15/60


=1/4


Time taken together: Time = 1 divide ¼ = 4 days


Ans: 4 days


2. A can complete a work in 20 days and B can complete the same work in 30 days. How many days will they take if they work together?


Soln


Work rates per day:



  • A = 1/20 per day

  • B = 1/30 per day


Combined work per day:


1/20+1/30 = (3+2)/60 = 5/60 =1/12


Time taken together: Time =1 divided 1/12 = 12 days


Ans: 12 days


3: Ram can complete a work in 10 days and Shyam can complete the same work in 15 days. How many days will they take if they work together?


Soln.


Work rates per day:



  • Ram = 1/10 per day

  • Shyam = 1/15 per day


Combined work per day: 1/10 + 1/15 = (3 + 2)/30 = 5/30 = 1/6


Time taken together: Time = 1 divide 1/6 = 6 days


Ans: 6 days


4: A car runs at a speed of 16 km/h. How much time will it take to cover a distance of 96 km ?


Solution:


Time = Distance / Speed = 96/16 = 6 hours


Ans: 6 hours


5. A boat travels 12 km upstream (against the current) in 48 minutes. If the speed of the current is 2 km/h, what is the boat’s speed in still water ?


Solution :



  • Convert time to hours: 48 minutes = 48/60 = 0.8 hours.

  • Upstream speed = distance/time = 12/0.8 km/h.


→ Calculate: 12÷0.8 =12×10/8 = 12×1.25 = 15 km/h



  • Let v = boat speed in still water. Upstream speed = v − current = v-2.


→ So, v−2 =15.



  • Solve: v=15+2=17 km/h.


Ans: 17 km/h (boat’s speed in still water)


6. Ram, Shyam, and Mohan together can complete a work in 12 days. Ram and Mohan together can complete it in 60 days. How many days will Shyam alone take to complete the work ?


Soln


Work rates per day:



  • Ram + Shyam + Mohan = 1/12 per day

  • Ram + Mohan = 1/60 per day


Shyam’s 1-day work:


= (Ram + Shyam + Mohan) − (Ram + Mohan)


= 1/12-1/60  = 5-1/60 = 4/60 = 1/15


Time taken by Shyam alone:


Time = 1divide 1/15 = 15 days


Ans: 15 days


7. If a car travels 40 km in 2 hours and 60 km in the next 2 hours, Average Speed = ?


Then,
Total Distance = 40 + 60 = 100 km
Total Time = 2 + 2 = 4 hours


Average Speed = Total Distance / Total Time = 100/4 = 25 km/h


Average Speed = 25 km/h


Important Points :



  • The average is always a middle value.

  • A very large or very small number can change the average up or down.

  • Think of average as equal sharing — dividing everything equally among all parts.


8. A man covers 80% of the distance between Delhi and Agra in 4 hours at a speed of 45 km/h. Find the total distance between Delhi and Agra.


Options: A) 210 km  B) 180 km  C) 240 km  D) 225 km


Given:



  • Speed = 45 km/h

  • Time = 4 hours
     Distance covered = 45 × 4 = 180 km


This 180 km is 80% of the total distance.
So, Total distance=180×100 / 80 = 225 km


Ans: D) 225 km


9: If 5 cats catch 5 mice in 5 days, then 100 cats will catch 100 mice in how many days ?


Options:
(a) 1 day  (b) 5 days  (c) 20 days  (d) 100 days


Explanation:
5 cats → 5 mice in 5 days
So, 1 cat → 1 mouse in 5 days
Therefore, 100 cats → 100 mice in 5 days (since all work at the same rate).


Ans: (b) 5 days


10. Train A crosses a stationary train B in 50 seconds and a pole in 20 seconds, both at the same speed. If the length of train A is 240 meters, find the length of stationary train B.


Options: A. 260 meters  B. 300 meters  C. 360 meters  D. Insufficient data


Given:



  • Train A crosses a stationary train B in 50 seconds.

  • Train A crosses a pole in 20 seconds.

  • Length of Train A = 240 meters.


We have to find the length of Train B.


Find the speed of Train A


When Train A crosses a pole, only its own length is covered.


Speed of A = Distance / Time = 240/20 = 12 m/s


When Train A crosses Train B


Total distance covered = Length of A + Length of B
Time = 50 seconds


Distance = Speed × Time 


240 + Length of B = 12 × 50


240 + Length of B = 600


Length of Train B


Length of B = 600 − 240 = 360 meters


Ans: C. 360 meters