Trial Test 3 : 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 and B can complete a work in 20 days, B and C can complete it in 30 days, and C and A can complete it in 40 days. If A alone does the work, in how many days will A complete it ?


Soln


Total work = 120, LCM of 20, 30, 40 = 120


Pair efficiencies:



  • A + B = 120/20 = 6

  • B + C = 120/30 = 4

  • C + A = 120/40 = 3


Add them: 6 + 4 + 3 = 13
This is 2 × (A + B + C)


So, A + B + C = 13 ÷ 2 = 6.5


A’s efficiency = (A+B+C) - (B+C)
= 6.5 − 4 = 2.5


Time taken by A = Total work / A’s efficiency
= 120 ÷ 2.5 = 48 days


2. Ram can finish a work in 20 days and Shyam can finish it in 30 days. Both work together for 8 days, then Ram leaves. How many days will Shyam take to finish the remaining work ?


Soln


Ram + Shyam do 1/20+1/30 = 1/12 work/day.


In 8 days they do 8/12 = 2/3.


Remaining 1/3 work ÷ Shyam’s rate 1/30 = (1/3)/(1/30) = 10 days.


Ans: 10 days


3: A monkey climbs a slippery pole 13 meters high. Every first second it climbs 3 meters, and in the next second, it slips down 1 meter. In how many seconds will it reach the top ?


Options:
(a) 11 seconds  (b) 10 seconds  (c) 9 seconds  (d) 8 seconds


Soln
In 2 seconds, monkey climbs (3 – 1) = 2 meters effectively.
To reach 11 meters (since in the last jump it won’t slip),
11 ÷ 2 = 5 pairs of seconds = 10 seconds → reached 11 m,
Then climbs last 3 meters in next 1 second.


Total = 10 + 1 = 11 seconds


Ans: (a) 11 seconds


4. Ram and Shyam can do a work in 20 days, Shyam and Mohan can do it in 24 days, Mohan and Ram can do it in 30 days.


In how many days will all three together complete the work ?


Options: (a) 6 Days  (b) 10 Days  (c) 14 Days   (d) 16 Days


Soln


Work rates



  • Ram + Shyam = 1/20 work per day

  • Shyam + Mohan = 1/24 work per day

  • Mohan + Ram = 1/30 work per day


Add all three :


= 1/20​ + 1​/24 + 1​/30, LCM = 120


= 6/120​ + 5/120​ + 4/120 ​= 15​/120


This value is double of (Ram + Shyam + Mohan), So divide by 2:.


15/120 ​÷ 2 = 1​/16, So all three together take: 16 days


5. A can complete a work in 10 days and B can complete the same work in 15 days. If they work alternately one day each, in how many days will the work be completed ?


Soln:


Work done per day:



  • A = 1/10 per day

  • B = 1/15 per day


Work done in 2 days (1 day A + 1 day B):


1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6 work in 2 days


Total cycles needed:



  • Total work = 1

  • Each 2-day cycle completes 1/6

  • Number of 2-day cycles = 6 → 6 × 2 = 12 days


Ans: 12 days


6. Ram completes 1/4 of the work in 5 days. Mohan completes 1/6 of the work in 5 days. If both work together, in how many days will they finish the whole work ?


Soln


Their 1-day work


Ram:1/4 work in 5 days, So in 1 day = (1/4) ÷ 5 = 1/20


Mohan: 1/6 work in 5 days, So in 1 day = (1/6) ÷ 5 = 1/30


Add both efficiencies


Ram + Mohan in 1 day = 1/20 + 1/30 = (3 + 2) / 60 = 5/60 = 1/12


Total time : Together they do 1/12 work per day →
So full work = 12 days


Ans: 12 days


7. A and B can complete a work in 20 days, B and C can complete it in 30 days, and C and A can complete it in 40 days. If A alone does the work, in how many days will A complete it ?


Soln


Total work = 120, LCM of 20, 30, 40 = 120


Pair efficiencies:



  • A + B = 120/20 = 6

  • B + C = 120/30 = 4

  • C + A = 120/40 = 3


Add them: 6 + 4 + 3 = 13
This is 2 × (A + B + C)


So, A + B + C = 13 ÷ 2 = 6.5


A’s efficiency = (A+B+C) - (B+C)
= 6.5 − 4 = 2.5


Time taken by A = Total work / A’s efficiency
= 120 ÷ 2.5 = 48 days


8: A person covers a distance of 48 km in 4 hours. Find his speed.


Solution:


Speed = Distance / Time = 48/4 = 12 km/h


Ans: 12 km/h


9: A train runs at a speed of 22 km/h. How much distance will it cover in 8 hours ?


Solution:


Distance = Speed × Time = 22×8 = 176 km


Ans: 176 km


10. A boat covers 20 km downstream in 2 hours and the same 20 km upstream in 5 hours. What is the boat’s speed in still water ?


Solution :



  • Downstream speed =20/2=10 km/h.

  • Upstream speed =20/5=4 km/h

  • Let v = still-water speed and c = current speed.


→   Downstream: v+c =10.


→   Upstream: v−c = 4.



  • Add the two equations: (v+c)+(v−c)=10+4⇒2v=14

  • So v =14÷2 = 7 km/h.


Ans: 7 km/h (boat’s speed in still water)