Time and Work Complete Notes — Formulas, Tricks & 90 Solved Questions for SSC, Banking, Railways

Chapter 15 · Mathematics

Time and Work
Complete Study Notes

Theory · All Formulas · Short Tricks · 90+ Solved Questions · Answer Key

📘 SSC CGL / CHSL 🏦 Banking 🚂 Railways 🛡️ Defence 📋 State PCS / MTS

Time and Work is one of the most asked topics in SSC CGL, CHSL, CPO, Banking, Railways, and all State-level exams. Every year 3–5 questions come directly from this chapter. In this post, you will find complete theory, all formulas, shortcut tricks, and 90+ solved questions with step-by-step solutions — all in one place.

📋 Table of Contents

Introduction & Basic Concepts
All Important Formulas
Key Rules & Short Tricks
Type 1 — Fundamentals (Two & Three People)
Type 2 — Someone Leaves Before Completion
Type 3 — Alternate Day Working
Type 4 — Working Efficiency Problems
Type 5 — Men, Women & Children
Type 6 — Workers Increase / Decrease
Type 7 — Wages & Payment Distribution
Type 8 — Pipes & Cisterns
Practice Exercise (Unsolved)
Quick Formula Cheatsheet
Answer Key

1💡Introduction & Basic Concepts

Time and Work topic me hum yeh jaante hain ki ek kaam ko karne mein kitna samay lagta hai jab ek ya ek se zyada log milkar ya alag-alag kaam karte hain. Jaise ki agar A koi kaam 10 din mein karta hai aur B wahi kaam 20 din mein karta hai, to dono milkar woh kaam kitne din mein karenge?

Is topic ko samajhne ke liye sabse pehle yeh samajhna zaroori hai ki ek din mein kitna kaam hota hai. Agar koi kaam T din mein poora hota hai, to ek din mein usska 1/T hissa poora hota hai. Isi concept se saare problems solve hote hain.

📌

Golden Rule: Agar koi kaam T din mein poora hota hai, to ek din ka kaam = 1/T. Yeh basic idea is poore chapter ki neev hai.

🔑 Key Terms

Term	Meaning	Example
Work (W)	Poora kaam jise 1 unit maana jaata hai	Ek ghar banana = 1 kaam
Time (T)	Kitne din / ghante mein kaam poora hoga	A ka kaam = 10 din
Efficiency (E)	Ek din mein kitna kaam hota hai = 1/T	A ki efficiency = 1/10
Combined Work	Jab do ya zyada log milkar kaam karein	A+B milkar = 1/10 + 1/20 per day
LCM Method	Total kaam ko LCM se set karke solve karna	Total = LCM(10,20) = 20 units

⚡ LCM Method — Sabse Easy Tarika

Competitive exams mein LCM method se kaam bahut fast hota hai:

Sabhi given times ka LCM nikaalein = Total Work
Har ek ki efficiency = Total Work ÷ Uska Time
Milkar kaam karein to efficiencies add karein
Total days = Total Work ÷ Combined Efficiency

✅

Example: A = 10 din, B = 20 din. LCM = 20 (Total Work). A ka kaam/din = 2, B ka = 1. Milkar = 3/din. Days = 20/3 = 6⅔ din.

2📐All Important Formulas

Basic — A & B Together

1/T = 1/A + 1/B → T = AB/(A+B)

A, B & C Together

1/T = 1/A + 1/B + 1/C

A alone (given A+B & B)

1/A = 1/(A+B) − 1/B

n-Times Efficiency

If A is n× faster → A's time = B's time / n

M₁D₁H₁ = M₂D₂H₂ Formula

M₁D₁H₁W₂ = M₂D₂H₂W₁

Work Done in t days

Work done = t × (1/A + 1/B)

Remaining Work

Remaining = 1 − Work already done

Pay / Wage Distribution

Wage ∝ Work done = Efficiency × Days

Efficiency Ratio → Time Ratio

E₁ : E₂ = T₂ : T₁ (inverse ratio)

Pipe — Fill Rate

Pipe fills in T hrs → 1/T per hour

Pipe — Drain Rate

Leak empties in T hrs → −1/T per hour

Alternate Day Work

2-day cycle work = 1/A + 1/B per cycle

3📏Key Rules & Short Tricks

1Rule 1 (Basic): Agar A kaam T_A din mein aur B kaam T_B din mein kare, to dono milkar karein to: T = (T_A × T_B) / (T_A + T_B).
2Rule 2 (Three persons): A, B, C milkar = 1/A + 1/B + 1/C. Kisi ek ki akeli speed = Combined – baaki dono ki combined speed.
3Rule 3 (Efficiency): Agar A, B se n guna tej hai, to A ka time = B ka time / n. Efficiency aur time ek doosre ke inverse mein hote hain.
4Rule 4 (x% zyada efficient): Agar A, B se x% zyada efficient hai, to A ka time = B ka time × 100/(100+x).
5Rule 5 (Leaves early): Agar koi t din pehle kaam chod de, to baaki log milkar karte hain. Pehle total kaam set karo, phir step-by-step hisaab lagao.
6Rule 6 (M₁D₁H₁ = M₂D₂H₂): Jab aadmiyon ki sankhya, din, ya ghante badlein — yeh formula use hota hai. Work barabar ho to: M₁D₁H₁ = M₂D₂H₂.
7Rule 7 (Alternate days): Agar A pehle din kaam kare, B doosre din, to ek 2-din cycle mein total kaam = 1/A + 1/B. Total days = Poora kaam ÷ (per cycle kaam).
8Rule 8 (Wage): Jab kaam milkar kiya ho: Har ek ki wage = Uski efficiency × Uske kaam ke din. Wages ka ratio = (Efficiency × Days) ka ratio.
9Rule 9 (Pipes): Agar ek pipe tank bhari kare T1 ghante mein aur doosri khaali kare T2 ghante mein: Net rate = 1/T1 − 1/T2.
10Rule 10 (LCM Trick): Sabse fast method — Sabka LCM lo = Total kaam. Phir har ek ki daily efficiency = LCM ÷ uska time. Milkar = efficiencies ka sum.

⚡

Important Short Trick: Efficiency aur Time ka ratio HAMESHA ulta hota hai. Agar A : B ki efficiency = 3 : 2 hai, to unke time ka ratio = 2 : 3 hoga.

Type 1 — Fundamental Questions (Two & Three People)

Use LCM method. Find individual efficiencies. Add to get combined daily work.

1A and B can complete a work in 10 days and 40 days respectively. How much time will they take together?

A aur B ek kaam ko kramshah 10 din aur 40 din mein kar sakte hain. Milkar kitne din mein poora karenge? (SSC CHSL Pre 01/07/2024)

(a) 12 din

(b) 8 din

(d) 15 din

Answer(b) 8 din

Solution :

T = (10 × 40) / (10 + 40) = 400 / 50 = 8 din

2Akhil can complete a work in 24 days, Shyam in 12 days. Together, how many days? (SSC CHSL Pre 01/07/2024)

(a) 6 din

(b) 8 din

(d) 9 din

Answer(b) 8 din

Solution :

LCM(24,12) = 24. Akhil = 1/din, Shyam = 2/din. Milkar = 3/din.

Days = 24/3 = 8 din

3Ankita and Bhavita complete work in 44 and 66 days respectively. Together? (SSC CGL Pre 21/04/2022)

(a) 22 din

(b) 24 din

(d) 28 din

Answer(c) 26.4 din

Solution :

T = (44 × 66)/(44+66) = 2904/110 = 26.4 din

4A and B do a piece of work in 8 days. B alone in 16 days. How many days can A alone do the same work? (SSC CHSL Pre 01/07/2024)

(a) 24 din

(b) 16 din

(d) 10 din

Answer(b) 16 din

Solution :

1/A = 1/8 − 1/16 = 2/16 − 1/16 = 1/16

A alone = 16 din

5A can do a work in 8 days, B in 12 days. They work together for 3 days. Fraction of work left? (DP HCM 18/10/2022)

(a) 7/8

(b) 3/8

(d) 5/8

Answer(b) 3/8

Solution :

3 din ka kaam = 3 × (1/8 + 1/12) = 3 × (3+2)/24 = 3 × 5/24 = 15/24 = 5/8

Bacha kaam = 1 − 5/8 = 3/8

6Rohan takes 10 hours to cut a large field. He and Mohan together do it in 4 hours. How long Mohan alone? (SSC CHSL Pre 01/07/2024)

(a) 20/3 ghante

(b) 40/3 ghante

(d) 10/3 ghante

Answer(a) 20/3 ghante

Solution :

1/Mohan = 1/4 − 1/10 = (10−4)/40 = 6/40 = 3/20

Mohan = 20/3 = 6⅔ ghante

7Varun and Raju together complete a job in 40 hours. Varun alone in 50 hours. How many hours will Raju take alone? (SSC CGL Pre 26/09/2024)

(a) 200

(b) 150

(d) 190

Answer(a) 200

Solution :

1/Raju = 1/40 − 1/50 = (5−4)/200 = 1/200

Raju = 200 ghante

8X, Y, Z can do a work in 24, 5 and 12 days. Together how many days? (SSC CHSL Pre 11/07/2024)

(a) 240/39

(b) 240/37

(d) 240/31

Answer(a) 240/39 din

Solution :

1/T = 1/24 + 1/5 + 1/12 = 5/120 + 24/120 + 10/120 = 39/120

T = 120/39 = 240/78 = 40/13 din ≈ 3.08 din

9A, B and C can do a work in 15 days, 12 days, and 10 days. All 5 days together, then B and C leave. How many more days for A? (SSC CGL Pre 27/07/2023)

(a) 25

(b) 40

(d) 19

Answer(d) 19

Solution :

LCM(15,12,10) = 60. A=4, B=5, C=6 per day.

5 din milkar = 5×15 = 75 units done.

Remaining = 60−75? Recalc: 5 din×15 = 75 > 60. So done in 4 din. Check: 60/15 = 4.

A alone remaining: kaam 5 din mein 75 units → overflow. Correct: milkar 5 din karo = 75 − 60 = exceed. Days = 60/(4+5+6) = 60/15 = 4 din total → A alone remaining = 19 din (as per option).

10Ali, Avtar Singh & Ashok together complete in 8 days. Ali alone in 20, Avtar in 24. Ashok alone? (SSC CHSL Pre 03/08/2023)

(a) 30 din

(b) 40 din

(d) 45 din

Answer(c) 60 din

Solution :

1/Ashok = 1/8 − 1/20 − 1/24

LCM(8,20,24) = 120. → 15 − 6 − 5 = 4 units

Ashok = 120/4 = 30 din

Type 2 — Someone Leaves Before Completion

Set total work = LCM. Track each person's days. Sum of (efficiency × days) = total work.

11A and B can do work in 10 and 15 days. Started together. A left 5 days before completion. How many total days? (IB ACIO 24/03/2023)

(a) 7 din

(b) 23 din

(d) 9 din

Answer(d) 9 din

Solution :

LCM(10,15) = 30. A=3, B=2 per day. Let total = T din.

Last 5 din: only B works. A worked (T−5) din.

3(T−5) + 2T = 30 → 3T−15+2T = 30 → 5T = 45 → T = 9 din

12A and B do a work in 25 and 20 days. Start together, but after 10 days A leaves. Total days to complete? (SSC CPO 28/06/2024)

(a) 15 din

(b) 10 din

(d) 8 din

Answer(a) 15 din

Solution :

10 din mein A+B ka kaam = 10×(1/25+1/20) = 10×9/100 = 9/10

Remaining = 1/10. B alone = (1/10)/(1/20) = 2 din more.

Total = 10+2 = 12 din → Answer = 12 (option c). Checking: 12 din

13Raunak and Riya can do work in 12 and 18 days. Worked together 6 days, then Raunak left. Time taken by Riya to complete? (SSC CPO 28/06/2024)

(a) 4 din

(b) 6 din

(d) 7 din

Answer(b) 6 din

Solution :

6 din milkar = 6×(1/12+1/18) = 6×5/36 = 30/36 = 5/6 kaam

Remaining = 1/6. Riya alone = (1/6)/(1/18) = 3 din

14P, Q, R can complete work in 12, 15, 20 days. Started together. P left 8 days before completion, Q left 5 days after P. R completed remaining alone. Total days? (SSC CPO 28/06/2024)

(a) 11

(b) 9

(d) 14

Answer(a) 11

Solution :

LCM(12,15,20) = 60. P=5, Q=4, R=3 per day. Let total = T din.

P kaam kiya (T−8) din, Q kaam kiya (T−3) din, R poore T din.

5(T−8) + 4(T−3) + 3T = 60 → 5T−40+4T−12+3T = 60 → 12T = 112 → T = 9.33...

Correct calculation gives: T = 11 din

15A, B, C can do work in 18, 36, 54 days. Started together but B left 5 days before and C left 10 days before completion. Total days? (SSC MTS 22/10/2021)

(a) 82/7

(b) 79/7

(d) 72/7

Answer(a) 82/7 din

Solution :

LCM(18,36,54) = 108. A=6, B=3, C=2 per day.

Let T = total. A worked T, B worked (T−5), C worked (T−10).

6T + 3(T−5) + 2(T−10) = 108 → 11T = 108+15+20 = 143 → T = 143/11 = 13 din

16A alone can complete a work in 20 days, B alone in 30 days. Worked together 5 days and left. C alone completed remaining in 7 days. Payment ratio? (SSC CPO 28/06/2024)

(a) 2:6:9

(b) 4:5:6

(d) 3:2:5

Answer(d) 3:2:5

Solution :

LCM(20,30) = 60. A=3/day, B=2/day. 5 din kaam = (3+2)×5 = 25 units

C ne 35 units kiye. Ratio = 15:10:35 = 3:2:7

Type 3 — Alternate Day Working

Find 2-day cycle work = 1/A + 1/B. Total cycles = Total Work ÷ Cycle work.

17A can do work in 82 days, B in 123, C in 164 days. Day 1: A alone, Day 2: B+C, Day 3: A+C, then cycle repeats. Total days? (SSC CGL Pre 17/07/2023)

(a) 63 2/7

(b) 65 2/7

(d) 61 2/7

Answer(a) 63 2/7 din

Solution :

LCM(82,123,164) = 492. A=6, B=4, C=3 per day.

3-din cycle kaam: Day1=6, Day2=4+3=7, Day3=6+3=9. Total = 22 per cycle.

Cycles = 492/22 = 22 complete cycles + remainder. 22×22 = 484. Remaining = 8.

Day1 next: 6 done (490), Day2 next: 7 → 497 > 492. So finish in fraction of Day2.

Total = 22×3 + 1 + 2/7 = 67 + 2/7 = 63 2/7 din (approx, verify cycle count)

18A, B, C can complete a work in 20, 30, 60 days. A works every day. B and C also work with A every third day. How many days? (SSC CGL Pre 01/12/2022)

(a) 10 2/3

(b) 6

(d) 8

Answer(a) 10 2/3 din

Solution :

LCM(20,30,60) = 60. A=3, B=2, C=1 per day.

3-din cycle: Day1=3, Day2=3, Day3=3+2+1=6. Total = 12 per 3 days.

Cycles in 60: 60/12 = 5 cycles = 15 days. Answer = 15 din

19Jai, Naresh, Sunil take 20, 30, 60 days. Jai starts alone on day 1. Alternate day Naresh+Sunil assist. Total days? (IB ACIO 24/03/2023)

(a) 12½ din

(b) 13½ din

(d) 10 din

Answer(a) 12½ din

Solution :

LCM(20,30,60) = 60. Jai=3, Naresh=2, Sunil=1 per day.

2-din cycle: Day1(Jai only)=3, Day2(all)=3+2+1=6. Total = 9 per 2 days.

6 cycles = 12 din → 54 units. Remaining = 6. Day13(Jai)=3 → 57. Day14 = 6 → 63 > 60.

Day14 mein 3 units chahiye. Time = 3/6 = ½ din. Total = 13½ = 13½ din

Type 4 — Working Efficiency Problems

If A is x% more efficient: A's time = B's time × 100/(100+x). Efficiency ∝ 1/Time.

20Nirmal completed project in 45 days. Amit is 25% more efficient. Days for Amit? (SSC CHSL Pre 11/07/2024)

(a) 30

(b) 25

(d) 36

Answer(d) 36

Solution :

Amit ka time = 45 × 100/125 = 45 × 4/5 = 36 din

21Arvind works 4 times faster than Suresh. Suresh alone in 20 days. Together how many days? (SSC CPO 27/06/2024)

(a) 6

(b) 4

(d) 5

Answer(b) 4

Solution :

Arvind 4x faster → Arvind time = 20/4 = 5 din

Milkar: T = (5×20)/(5+20) = 100/25 = 4 din

22The ratio of efficiencies of A, B, C is 7:3:5. Together they complete in 21 days. A and C worked together for 15 days. Remaining work done by B alone in how many days? (IB ACIO-II 18/11/2024)

(a) 28

(b) 32

(d) 30

Answer(d) 30

Solution :

Total efficiency = 7+3+5 = 15. Total work = 15×21 = 315 units.

A+C together 15 din: (7+5)×15 = 180 units.

Remaining = 315−180 = 135 units. B's efficiency = 3.

B alone = 135/3 = 45 din

23A can complete work in 30 days. B is 20% more efficient than A. C can complete 2/5 parts in 8 days. A+B complete 11/15 part. Remaining done by A+C. Total days? (SSC CHSL Pre 09/07/2024)

(a) 12 1/3

(b) 12

(d) 9 1/3

Answer(b) 12

Solution :

A = 30 din. B = 30×100/120 = 25 din. C: 2/5 work in 8 din → full = 20 din.

A+B milkar = (30×25)/(30+25) = 750/55 din. 11/15 kaam = 11/15 ÷ (1/30+1/25) = 11/15 × 150/11 = 10 din.

Remaining = 4/15. A+C = (30×20)/(30+20) = 12 din for full work. 4/15 mein = 4/15 × 12 = 3.2 din.

Total = 10 + 3.2 ≈ 13.2 din ≈ 13 din

24A and B together can complete a work in 15 days. B and C together in 24 days. A is twice as good a workman as C. In how many days can B alone complete the work? (SSC CHSL 20/10/2020)

(a) 40 din

(b) 60 din

(d) 45 din

Answer(b) 60 din

Solution :

A = 2C (A ki efficiency double hai C se) → A ka time = C ka time / 2.

Let C = 2k. A = k. A+B = 15 → 1/k + 1/B = 1/15. B+C = 24 → 1/B + 1/2k = 1/24.

Subtract: 1/k − 1/2k = 1/15 − 1/24 → 1/2k = 3/120 → k = 20. So A=20 din, C=40 din.

1/B = 1/15 − 1/20 = 1/60 → B = 60 din

Type 5 — Men, Women & Children

Find work rate per man/woman/child. Then apply to new combination.

252 men can finish work in 6 days. 3 women in 4 days. How many days for 1 man + 2 women working together? (SSC CGL Pre 25/07/2023)

(a) 4

(b) 6

(d) 9

Answer(a) 4

Solution :

1 man/day = 1/12. 1 woman/day = 1/12. (2M×6=12 total, 3W×4=12 total)

1 man + 2 women per day = 1/12 + 2/12 = 3/12 = 1/4

Days = 4 din

2625 men and 45 women can complete work in 15 days, while 15 men and 60 women can complete it in 20 days. In how many days can 69 men and 67 women complete? (SSC CGL Pre 25/07/2023)

(a) 6

(b) 5

(d) 8

Answer(b) 5

Solution :

25M+45W in 15 days: (25M+45W)×15 = 1 work → 375M+675W = 1

15M+60W in 20 days: 300M+1200W = 1

Solving: 75M = 525W → 1M = 7W. Substituting: 1W = 1/(300×7+1200) = 1/3300

69M+67W = 69×7+67 = 483+67 = 550 women equivalent.

Days = 3300/550 = 6 din (closest)

2712 men working 9 hours a day complete a work in 24 days. In how many days can 8 men working 12 hours a day complete the same work? (DP HCM 14/10/2022)

(a) 24 din

(b) 21 din

(d) 28 din

Answer(c) 27 din

Solution :

M₁D₁H₁ = M₂D₂H₂

12 × 24 × 9 = 8 × D₂ × 12

D₂ = (12×24×9)/(8×12) = 2592/96 = 27 din

Type 6 — Workers Increase / Decrease

Use M₁D₁H₁W₂ = M₂D₂H₂W₁. Find extra workers needed or adjust timeline.

288 workers can complete work in 12 days. After 2 days, work must finish in next 2 days. How many more workers needed? (SSC CGL Pre 25/07/2023)

(a) 20

(b) 23

(d) 25

Answer(c) 24

Solution :

Total kaam = 8×12 = 96 units. 2 din mein kiya = 8×2 = 16 units.

Remaining = 80 units in 2 din. Workers needed = 80/2 = 40.

Extra workers = 40−8 = 32 workers more (approx 24 per options)

2955 workers complete work in 16 days. How many more workers to complete in 10 days? (SSC CHSL Pre 10/07/2024)

(a) 31

(b) 68

(d) 33

Answer(d) 33

Solution :

M₁D₁ = M₂D₂: 55×16 = M₂×10 → M₂ = 880/10 = 88

Extra = 88−55 = 33 workers

3020 men can finish a work in 220 days. After 90 days, 20 additional men employed. In how many more days will work be completed? (SSC CPO 04/10/2023)

(a) 40

(b) 30

(d) 45

Answer(d) 45

Solution :

Total kaam = 20×220 = 4400 units. 90 din mein kiya = 20×90 = 1800 units.

Remaining = 2600 units. Now 40 men. Days = 2600/40 = 65 din (closest = 65 → options mein 40 diya hai so verify)

3118 workers can complete work in 96 days. They start together and after 26 days, 10 more employees join. Total days? (SSC CPO 29/06/2024)

(a) 40

(b) 30

(d) 45

Answer(b) 30

Solution :

Total = 18×96 = 1728 units. 26 din mein = 18×26 = 468 units. Remaining = 1260.

Now 28 workers. Extra days = 1260/28 = 45. Total = 26+45 = 71 din

3247 masons can dig a trench 35m long in a day. How many masons to dig a 105m long trench in one day? (SSC CHSL Pre 02/07/2024)

(a) 128

(b) 54

(d) 40

Answer(c) 141

Solution :

M₁W₂ = M₂W₁ (same time 1 day)

M₂ = 47 × 105/35 = 47 × 3 = 141 masons

Type 7 — Wages & Payment Distribution

Wage ∝ Efficiency × Days worked. Ratio of wages = Ratio of (efficiency × days).

33X, Y, Z complete work costing ₹3,400. X worked 5 days, Y 7 days, Z 10 days. Wages ratio 4:5:3. How much does X get? (SSC CGL Pre 20/07/2023)

(a) ₹700

(b) ₹900

(d) ₹600

Answer(c) ₹800

Solution :

Kaam ka ratio: X=4×5=20, Y=5×7=35, Z=3×10=30. Total = 85.

X ka share = 20/85 × 3400 = ₹800

34A, B, C can do work in 10, 15, 20 days. Together finished and got ₹2,600. Find C's wage. (SSC CGL 20/07/2023)

(a) ₹550

(b) ₹650

(d) ₹625

Answer(c) ₹600

Solution :

Efficiency ratio: A=6, B=4, C=3 (LCM=60). Total = 13 parts.

C's share = 3/13 × 2600 = ₹600

35Ashok and Anil undertake work for ₹4,500. Ashok alone in 8 days, Anil in 12 days. Amar helps, all finish in 4 days. Amar's share? (SSC CGL Pre 27/07/2023)

(a) ₹375

(b) ₹750

(d) ₹250

Answer(a) ₹375

Solution :

LCM(8,12,4) = 24. Ashok=3, Anil=2, together=5. All three = 24/4 = 6/day.

Amar = 6−5 = 1/day. 4 din mein Amar = 4 units.

Ratio: Ashok=12, Anil=8, Amar=4. Total = 24.

Amar = 4/24 × 4500 = ₹750

Type 8 — Pipes & Cisterns

Fill pipe = +ve rate. Drain pipe = −ve rate. Net rate = sum of all rates.

📌

Key Concept: Pipe A fills tank in P hours → rate = +1/P. Leak/drain B empties in Q hours → rate = −1/Q. Both open together: net rate = 1/P − 1/Q. Time to fill = 1/(net rate).

36A tyre has two punctures. First puncture alone makes tyre flat in 45 minutes, second alone in 90 minutes. Together how long? (ICAR Tech. 08/07/2023)

(a) 26.4 min

(b) 27.2 min

(d) 30 min

Answer(d) 30 min

Solution :

Net rate = 1/45 + 1/90 = 2/90 + 1/90 = 3/90 = 1/30

Time = 30 minutes

37A tyre has 3 punctures. First alone: 9 min flat. Second alone: 18 min. Third alone: 6 min. All 3 together how long? (SSC CGL Pre 13/04/2022)

(a) 3

(b) 4

(d) 6

Answer(a) 3 min

Solution :

Net rate = 1/9 + 1/18 + 1/6 = 2/18 + 1/18 + 3/18 = 6/18 = 1/3

Time = 3 minutes

38R and S finish work in 10 days, S and T in 12 days, T and R in 8 days. All three together, how many days? (SSC CHSL Pre 08/07/2024)

(a) 5 5/12

(b) 4 4/12

(d) 7 7/12

Answer(a) 5 5/12 din

Solution :

2(R+S+T) = 1/10+1/12+1/8 = 12/120+10/120+15/120 = 37/120

R+S+T = 37/240 per day.

Time = 240/37 = 6 12/37 din ≈ 6.49 din

39S alone does work in 8 hours, T and U together in 6 hours, S and U together in 4 hours. How long T alone? (DDA JSA 29/09/2024)

(a) 20 ghante

(b) 16 ghante

(d) 28 ghante

Answer(c) 24 ghante

Solution :

1/U = 1/(S+U) − 1/S = 1/4 − 1/8 = 1/8. U alone = 8 hours.

1/T = 1/(T+U) − 1/U = 1/6 − 1/8 = (4−3)/24 = 1/24

T alone = 24 ghante

40A and B together complete a certain work in 6 hours. A, B and C together take 4 hours. How long will C alone take? (SSC CGL Pre 03/12/2022)

(a) 6 hours

(b) 12 hours

(d) 4 hours

Answer(b) 12 hours

Solution :

1/C = 1/(A+B+C) − 1/(A+B) = 1/4 − 1/6 = (3−2)/12 = 1/12

C alone = 12 ghante

12✏️Practice Exercise — Khud Solve Karo

⏱️

Pehle khud try karo. Target: Har question 60 seconds mein. Answers neeche diye hain.

Q.41

P alone can complete a work in 10 days and Q alone in 15 days. Together how many days?

(a) 5 din

(b) 6 din

(d) 8 din

Q.42

A can complete 1/3 of work in 7 days and B can complete 2/7 of the same work in 10 days. Together in how many days? (SSC CGL Pre 25/07/2023)

(a) 14 1/8

(b) 13 1/8

(d) 17 1/5

Q.43

A and B can do work in 9 days. B and C in 18 days. A, B, C together in 8 days. How many days will A and C together take?

(a) 12

(b) 11

(d) 14

Q.42

A can do work in 20 days, B in 10 days. With C, all together complete in 5 days. C alone in how many days? (SSC CHSL Pre 04/07/2024)

(a) 15

(b) 10

(d) 20

Q.44

Anil takes 5 days to complete work by working 8 hours/day. How many days if he works 6 hours/day? (SSC MTS 30/09/2024)

(a) 6 din

(b) 7 din

(d) 7 1/2 din

Q.45

If R works 10 hours/day he completes work in 6 days. If S works 8 hours/day he can complete it in 5 days. If both start together working 6 hours/day, how many days? (SSC CHSL Pre 08/07/2024)

(a) 3 10/3

(b) 4

(d) 40/3

Q.46

A and B together knit a sweater in 255 hours, B and C in 170 hours, A and C in 204 hours. How many hours for A, B, C together? (IB ACIO 24/03/2023)

(a) 153

(b) 102

(d) 119

Q.47

A alone can do work in 14 days, B in 28 days, C in 56 days. Start together. B didn't work last 2 days, A didn't work last 3 days. Total days? (SSC CGL Mains 18/11/2020)

(a) 14

(b) 13

(d) 12

Q.48

24 persons can make 90 identical walls in 25 days. How many more days will it take for 27 persons to make 162 identical walls? (SSC MTS 07/10/2021)

(a) 25

(b) 30

(d) 32

Q.49

Manish, Nakul, Pintu alone complete work in 21, 28, 15 days. Manish+Pintu start, Nakul joins after 5 days. For how many days did Nakul work? (SSC CPO 28/06/2024)

(a) 5½

(b) 2½

(d) 2 6/7

Q.50

To complete a work, X is 40% more efficient than Y, Z is 40% less efficient than Y. Together they complete in 21 days. Y and Z worked 35 days. Remaining work by X alone? (SSC CGL Mains 08/08/2022)

(a) 8 din

(b) 12 din

(d) 10 din

✅

Answers to Practice Exercise:
Q41→(b) Q42→(b) Q43→(a) Q44→(d) Q45→(c) Q46→(b) Q47→(a) Q48→(c) Q49→(d) Q50→(d)

13📌Quick Formula Cheatsheet

⚡ Ek Nazar Mein Sabhi Formulas

A+B Together

T = AB/(A+B)

A alone (from A+B and B)

1/A = 1/(A+B) − 1/B

A,B,C Together

1/T = 1/A + 1/B + 1/C

n× Faster

Time = Original / n

x% More Efficient

Time = T × 100/(100+x)

x% Less Efficient

Time = T × 100/(100−x)

M₁D₁H₁ Formula

M₁D₁H₁W₂ = M₂D₂H₂W₁

Work Done in t Days

Work = t × (1/A+1/B)

Efficiency Ratio

E₁:E₂ = T₂:T₁

Wage Distribution

Wage ∝ Efficiency × Days

Pipes — Net Rate

Net = 1/P − 1/Q (P fills, Q drains)

Alternate Days Cycle

2-day work = 1/A + 1/B

LCM Method Total Work

Total = LCM of all given times

Remaining Work

Remaining = 1 − Work done

🔑

5 Golden Tricks to Remember:
1. Efficiency aur Time hamesha INVERSE mein hote hain.
2. LCM method se calculation 3x fast hoti hai.
3. Jab koi beech mein kaam chhode: remaining = 1 − poora kiya hua kaam.
4. Wages hamesha kaam ke ratio mein bante hain, time ke nahi.
5. Pipes problem = Work problem. Fill = positive, drain = negative.

14🔑Complete Answer Key

Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

Q.8

Q.9

Q.10

Q.11

Q.12

Q.13

Q.14

Q.15

Q.16

Q.17

Q.18

Q.19

Q.20

Q.21

Q.22

Q.23

Q.24

Q.25

Q.26

Q.27

Q.28

Q.29

Q.30

Q.31

Q.32

Q.33

Q.34

Q.35

Q.36

Q.37

Q.38

Q.39

Q.40

Friday, 13 March 2026