About this quiz
50 questions covering every section of the note on one day's work, working together, the LCM method and efficiency, work and wages, men-days and man-hours, pipes and cisterns and the step-by-step method.
This Lok Sewa practice set has 50 multiple-choice questions (Subject: Maths and IQ · For: Kharidar, Nayab Subba, Section Officer · Level: Medium). Take the quiz above first; after that, use the study list below to revise every question with its correct answer and a short explanation.
Study list: all 50 questions with answers and explanations
Sunita can finish a job in 15 days. What part of the job does she finish in 6 days?
- A) 1/6
- B) 2/5 ✔
- C) 3/5
- D) 2/3
Why: One day's work = 1/15. In 6 days: 6/15 = 2/5.
Ramesh does 1/8 of a job each day. How many days does he need to finish the whole job?
- A) 4 days
- B) 7 days
- C) 8 days ✔
- D) 16 days
Why: If one day's work is 1/n, the job takes n days. So 8 days.
A can do a piece of work in 10 days and B in 15 days. In how many days can they finish it together?
- A) 12.5 days
- B) 5 days
- C) 6 days ✔
- D) 25 days
Why: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so 6 days. Formula: 10 × 15/25 = 6.
A, B and C can do a job in 20, 30 and 60 days. In how many days can all three finish it together?
- A) 10 days ✔
- B) 15 days
- C) 12 days
- D) 36.7 days
Why: 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10, so 10 days.
A and B together can do a work in 10 days. A alone can do it in 15 days. How long will B alone take?
- A) 25 days
- B) 5 days
- C) 20 days
- D) 30 days ✔
Why: B's one day's work = 1/10 − 1/15 = 3/30 − 2/30 = 1/30, so 30 days.
A and B can do a job in 12 days, B and C in 15 days, and C and A in 20 days. How long will A, B and C take working together?
- A) 10 days ✔
- B) 5 days
- C) 15 days
- D) 8 days
Why: 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. This is 2 × (A + B + C), so A + B + C = 1/10, that is 10 days.
A can do half of a job in 5 days, and B can do the whole job in 15 days. In how many days can they finish the whole job together?
- A) 3.75 days
- B) 6 days ✔
- C) 10 days
- D) 7.5 days
Why: A needs 10 days for the full job. Together: 10 × 15/(10 + 15) = 150/25 = 6 days.
A takes 12 days and B takes 24 days to do a job. Using the LCM method with total work 24 units, how many units do they do together in one day?
- A) 2 units
- B) 4 units
- C) 36 units
- D) 3 units ✔
Why: A does 24 ÷ 12 = 2 units and B does 24 ÷ 24 = 1 unit a day. Together 3 units a day.
A can do a job in 12 days and B in 18 days. They work together for 4 days and then A leaves. In how many more days will B finish the job?
- A) 8 days ✔
- B) 10 days
- C) 12 days
- D) 6 days
Why: LCM = 36 units; A does 3, B does 2 a day. In 4 days: 4 × 5 = 20 units. Left: 16 units, B takes 16 ÷ 2 = 8 days.
A is twice as efficient as B. Together they finish a job in 12 days. How long would B alone take?
- A) 18 days
- B) 24 days
- C) 36 days ✔
- D) 48 days
Why: Efficiency A : B = 2 : 1. Total work = (2 + 1) × 12 = 36 units. B does 1 unit a day, so 36 days.
A can finish a job in 20 days. He works on it for 5 days, and B finishes the rest in 9 days. How long would B take to do the whole job alone?
- A) 15 days
- B) 12 days ✔
- C) 11.25 days
- D) 18 days
Why: A does 5/20 = 1/4. B does the remaining 3/4 in 9 days, so the whole job takes 9 × 4/3 = 12 days.
A can do a job in 9 days. B is 50% more efficient than A. How many days will B take alone?
- A) 13.5 days
- B) 4.5 days
- C) 3 days
- D) 6 days ✔
Why: Efficiency A : B = 2 : 3, so B's time = 2/3 of A's time = 9 × 2/3 = 6 days.
A can do a job in 12 days and B in 18 days. They work together and are paid Rs 6,000. What is A's share?
- A) Rs 3,600 ✔
- B) Rs 2,400
- C) Rs 3,000
- D) Rs 4,000
Why: LCM = 36; A does 3 and B does 2 units a day, ratio 3 : 2. A's share = 6,000 × 3/5 = Rs 3,600.
A takes 8 days and B takes 12 days to do a job. With the help of C they finish it in 4 days and are paid Rs 3,600. What is C's share?
- A) Rs 1,200
- B) Rs 900
- C) Rs 600 ✔
- D) Rs 400
Why: LCM = 24; A 3, B 2 units a day. All three do 24 ÷ 4 = 6 units a day, so C does 1. Ratio 3 : 2 : 1, so C gets 3,600 × 1/6 = Rs 600.
18 men can build a wall in 25 days. How many days will 30 men take to build the same wall?
- A) 41.7 days
- B) 15 days ✔
- C) 12 days
- D) 20 days
Why: M1 × D1 = M2 × D2: 18 × 25 = 30 × D2, so D2 = 450 ÷ 30 = 15 days.
20 men can complete a job in 12 days. How many more men must join so that the job is completed in 8 days?
- A) 30
- B) 8
- C) 12
- D) 10 ✔
Why: Men needed = 20 × 12/8 = 30. Extra men = 30 − 20 = 10.
15 men working 8 hours a day finish a job in 12 days. How many days will 20 men working 9 hours a day take for the same job?
- A) 10 days
- B) 9 days
- C) 8 days ✔
- D) 6 days
Why: Total = 15 × 8 × 12 = 1,440 man-hours. Days = 1,440 ÷ (20 × 9) = 1,440 ÷ 180 = 8 days.
10 men build a 40 m wall in 6 days. How many days will 15 men take to build a 90 m wall of the same kind?
- A) 9 days ✔
- B) 13.5 days
- C) 6 days
- D) 8 days
Why: D2 = M1 × D1 × W2/(W1 × M2) = 10 × 6 × 90/(40 × 15) = 5,400/600 = 9 days.
Pipe A fills a tank in 10 hours and pipe B fills it in 15 hours. If both are opened together, how long will they take to fill it?
- A) 12.5 hours
- B) 5 hours
- C) 25 hours
- D) 6 hours ✔
Why: 1/10 + 1/15 = 3/30 + 2/30 = 1/6, so 6 hours.
An inlet pipe fills a tank in 8 hours and an outlet pipe empties it in 12 hours. If both are opened together on an empty tank, when will it be full?
- A) 4.8 hours
- B) 24 hours ✔
- C) 20 hours
- D) 4 hours
Why: 1/8 − 1/12 = 3/24 − 2/24 = 1/24, so 24 hours.
Pipes A and B fill a tank in 12 and 15 hours, and pipe C empties it in 10 hours. If all three are opened on an empty tank, how long will it take to fill?
- A) 4 hours
- B) 12 hours
- C) 20 hours ✔
- D) 15 hours
Why: LCM = 60 units. Per hour: 5 + 4 − 6 = 3 units. Time = 60 ÷ 3 = 20 hours.
A pipe can fill a tank in 6 hours, but because of a leak it takes 8 hours. How long will the leak alone take to empty the full tank?
- A) 24 hours ✔
- B) 14 hours
- C) 2 hours
- D) 48 hours
Why: Leak's rate = 1/6 − 1/8 = 4/24 − 3/24 = 1/24, so 24 hours.
Pipe A fills a tank in 20 minutes and pipe B in 30 minutes. Both are opened for 6 minutes, then A is closed. How many more minutes will B take to fill the tank?
- A) 12 minutes
- B) 15 minutes ✔
- C) 18 minutes
- D) 24 minutes
Why: LCM = 60 units; A 3, B 2 units a minute. In 6 minutes: 6 × 5 = 30 units. Left 30 units, B takes 30 ÷ 2 = 15 minutes.
In the step-by-step method, how is the work of an outlet pipe or a leak treated?
- A) It is added to the work of the inlet pipes
- B) It is ignored
- C) It is multiplied by the number of inlets
- D) It is subtracted from the work of the inlet pipes ✔
Why: Inlets add work and outlets or leaks remove it, so their work is subtracted.
Using the step-by-step method, after a team has done 3/5 of a job, it does 1/10 of the job each day. How many more days will it take to finish?
- A) 6 days
- B) 2 days
- C) 4 days ✔
- D) 5 days
Why: Work left = 1 − 3/5 = 2/5. Days = 2/5 ÷ 1/10 = 2/5 × 10 = 4 days.
A does a job in 6 days and B in 12 days. Together they take:
- A) 4 days ✔
- B) 9 days
- C) 3 days
- D) 18 days
Why: 1/6 + 1/12 = 1/4.
A does a job in 10 days and B in 15 days. Together:
- A) 6 days ✔
- B) 12.5 days
- C) 5 days
- D) 25 days
Why: 1/10 + 1/15 = 1/6.
A, B and C take 20, 30 and 60 days alone. Together they take:
- A) 10 days ✔
- B) 12 days
- C) 15 days
- D) 110 days
Why: 6/60 = 1/10.
A and B together take 8 days; A alone takes 12 days. B alone takes:
- A) 24 days ✔
- B) 20 days
- C) 4 days
- D) 16 days
Why: 1/8 − 1/12 = 1/24.
A does 1/5 of a job each day. Days to do 3/5 of it:
- A) 3 ✔
- B) 5
- C) 2
- D) 4
Why: 3 × 1/5.
A does 1/3 of a job in 4 days. Whole job takes:
- A) 12 days ✔
- B) 7 days
- C) 8 days
- D) 16 days
Why: 4 × 3.
A is twice as fast as B; B alone takes 30 days. Together they take:
- A) 10 days ✔
- B) 15 days
- C) 20 days
- D) 45 days
Why: A = 15 days.
6 men do a job in 8 days. 12 men take:
- A) 4 days ✔
- B) 16 days
- C) 6 days
- D) 2 days
Why: Inverse proportion.
10 men do a job in 12 days. How many men to do it in 8 days?
- A) 15 ✔
- B) 20
- C) 12
- D) 18
Why: 120 ÷ 8.
5 men finish a job in 20 days. 25 men will finish it in:
- A) 4 days ✔
- B) 100 days
- C) 5 days
- D) 10 days
Why: 100 man-days.
A alone takes 15 days. He works 5 days and B finishes the rest in 10 days. B alone takes:
- A) 15 days ✔
- B) 10 days
- C) 20 days
- D) 30 days
Why: B does 2/3 in 10 days.
A pipe fills a tank in 4 hours and another empties it in 6 hours. With both open, it fills in:
- A) 12 hours ✔
- B) 10 hours
- C) 2.4 hours
- D) 5 hours
Why: 1/4 − 1/6 = 1/12.
Pipes A and B fill a tank in 6 and 3 hours. Together:
- A) 2 hours ✔
- B) 4.5 hours
- C) 9 hours
- D) 1.5 hours
Why: 1/6 + 1/3 = 1/2.
A and B fill a tank in 10 and 15 hours; C empties it in 30 hours. All open, it fills in:
- A) 7.5 hours ✔
- B) 6 hours
- C) 10 hours
- D) 5 hours
Why: 4/30.
A tank normally fills in 5 hours but takes 6 hours due to a leak. The leak alone empties a full tank in:
- A) 30 hours ✔
- B) 11 hours
- C) 1 hour
- D) 15 hours
Why: 1/5 − 1/6 = 1/30.
A man does 1/4 of a job in a day. In 3 days he does:
- A) 3/4 ✔
- B) 1/2
- C) 1
- D) 1/3
Why: 3 × 1/4.
A and B each take 20 days alone. Together they take:
- A) 10 days ✔
- B) 20 days
- C) 40 days
- D) 5 days
Why: Half.
A takes 10 days and B 15 days. They are paid Rs 5,000 for the job together. A's share:
- A) Rs 3,000 ✔
- B) Rs 2,000
- C) Rs 2,500
- D) Rs 3,500
Why: Efficiency 3 : 2.
12 men working 8 hours a day finish in 10 days. 10 men working 12 hours a day finish in:
- A) 8 days ✔
- B) 10 days
- C) 12 days
- D) 6 days
Why: 960 man-hours.
A pipe fills 1/3 of a tank in 1 hour. Full tank in:
- A) 3 hours ✔
- B) 1/3 hour
- C) 2 hours
- D) 4 hours
Why: 3 × 1.
A takes 5 days and B 10 days. The efficiency ratio A : B is:
- A) 2 : 1 ✔
- B) 1 : 2
- C) 5 : 10
- D) 1 : 1
Why: Efficiency is inverse of time.
A takes 18 days and B 9 days. Together:
- A) 6 days ✔
- B) 13.5 days
- C) 27 days
- D) 9 days
Why: 1/18 + 2/18.
A and B take 12 days, B and C 15 days, C and A 20 days. All three together take:
- A) 10 days ✔
- B) 15 days
- C) 12 days
- D) 8 days
Why: Half of 1/12 + 1/15 + 1/20 = 1/10.
One pipe fills 1/8 and another 1/12 of a tank per hour. Together they fill it in:
- A) 4.8 hours ✔
- B) 10 hours
- C) 5 hours
- D) 20 hours
Why: 5/24 per hour.
A does 40% of a job in 8 days. The whole job takes:
- A) 20 days ✔
- B) 16 days
- C) 32 days
- D) 10 days
Why: 8 ÷ 0.4.