Trial Test 1 : 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 together can complete a work in 8 days. A and C together can complete it in 24 days. How many days will B alone take to complete the work ?
Soln:
Work rates per day:
- A + B + C = 1/8 per day
- A + C = 1/24 per day
B’s 1-day work:
B = (A+B+C)-(A+C) = 1/8 – 1/24 = 3−1/24 = 2/24 = 1/12
Time taken by B alone:Time = 1 divide 1/12 = 12 days
Ans: 12 days
2. Ram and Shyam together can complete a work in 20 days. Shyam alone can complete it in 60 days. How many days will Ram alone take to complete the work ?
Soln:
Work rates per day:
- Ram + Shyam = 1/20 per day
- Shyam = 1/60 per day
Ram’s 1-day work:
Ram :
= 1/20 -1/60
= (3-1)/60
= 2/60
= 1/30
Time taken by Ram alone:
Time = 1 divide 1/30 = 30 days
Ans: 30 days
3: A hostel has food for 3000 students for 70 days. After 10 days, 1000 more students join. For how many more days will the remaining food last ?
Soln:
- Total food = 3000 × 70 = 210,000
- Food used in 10 days = 3000 × 10 = 30,000
- Remaining food = 210,000 − 30,000 = 180,000
- Remaining students = 3000 + 1000 = 4000
- Remaining days = 180,000 ÷ 4000 = 45 days
Ans: 45 days
4. A military camp had food for 1500 soldiers for 45 days. After 15 days, 500 soldiers leave. For how many more days will the remaining food last ?
Given:
- 1500 soldiers → 45 days of food
- After 15 days, 500 soldiers leave → remaining 1000 soldiers
Remaining food : 1500 × 45 − 1500 × 15 = 67500 − 22500 = 45000 units
Remaining days for 1000 soldiers : 45000 ÷ 1000 = 45 days
Ans: 45 days
5. A hostel has food for 800 students for 40 days. If 200 more students join (total 1000), for how many days will the food last ?
Soln: Use Inverse Proportion: = Students × Days = Constant
= 800 × 40 = 1000 × D
= 32000 = 1000×D
= D = 32 days
Ans: 32 days
6. A military camp had food for 1500 soldiers for 20 days. If 500 more soldiers join (total 2000 soldiers), for how many days will the food last ?
Soln :
- 1500 soldiers → food for 20 days
- 2000 soldiers → food for D days
Use the formula: Men × Days = Constant
So,
1500 × 20 = 2000 × D
30000 = 2000D
D = 30000 / 2000
D = 15 days
Ans: 15 days
7. A completes a work in 16 days and B completes the same work in 48 days. Both start working together, and after 9 days B leaves the work. How much time will A take to finish the remaining work ?
Soln
A’s 1 day work = 1/16
B’s 1 day work = 1/48
Work done in 9 days together
A + B = 1/16 + 1/48 = 1/12
In 9 days → 9 × 1/12 = 3/4 work done
Remaining work
1 − 3/4 = 1/4
Time taken by A for 1/4 work
A does 1/16 per day
So time = 1/4 ÷ 1/16 = 4 days
Ans: 4 days
8. 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
9: 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
10. 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