Mandays, Time & Work
Quick Recap
- If a person completes work in x days, one-day work = 1/x.
- If A and B work together, combined work = A’s rate + B’s rate.
- Total work = rate × time.
- Time = total work / rate.
- Wages are divided in the ratio of work done.
- For man-days: Men × Days × Hours × Efficiency = Total work.
- If work is same, compare total work units on both sides.
Q1. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days can B finish the whole work alone?
Correct Option: C
Rationale:
Let A’s one-day work = a and B’s one-day work = b.
a + b = 1/30
A works for 16 days and B works for 44 days:
16a + 44b = 1
Substitute a = 1/30 – b:
16(1/30 – b) + 44b = 1
16/30 + 28b = 1
28b = 14/30
b = 1/60
So B alone can finish the work in 60 days.
Q2. A and B together can do a piece of work in 30 days. If A alone takes 50 days, in how many days will B alone do the work?
Correct Option: D
Rationale:
A + B’s rate = 1/30
A’s rate = 1/50
B’s rate = 1/30 – 1/50
= 5/150 – 3/150
= 2/150
= 1/75
So B alone will take 75 days.
Q3. C can do a work in 15 days while D can do the same work in 20 days. Both start together and after 4 days, D leaves. In how many more days will C finish the remaining work?
Correct Option: A
Rationale:
C’s rate = 1/15
D’s rate = 1/20
Work done together in 4 days:
4 × (1/15 + 1/20)
= 4 × 7/60
= 7/15
Remaining work = 8/15
C alone completes remaining work in:
8/15 ÷ 1/15 = 8 days.
Q4. A can complete a work in 12 days and B can complete the same work in 18 days. A and B start together, but after 4 days A leaves. C then joins B and together they finish the remaining work in 5 days. If the total wages paid are ₹7200 and wages are divided in proportion to work done, what is C’s share?
Correct Option: C
Rationale:
A’s rate = 1/12
B’s rate = 1/18
Work done by A and B in first 4 days:
4 × (1/12 + 1/18)
= 4 × 5/36
= 5/9
Remaining work = 4/9
B and C finish 4/9 work in 5 days:
B + C rate = 4/45
B’s rate = 1/18
C’s rate = 4/45 – 1/18 = 1/30
C works for 5 days:
C’s work = 5/30 = 1/6
C’s share = 1/6 × 7200 = ₹1200.
Q5. Three diggers dug a ditch of 324 m in 6 days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger’s work in 10 days is equal to the first digger’s work in 14 days. How many metres does the first digger dig per shift?
Correct Option: D
Rationale:
Let the first digger dig x metres per shift.
Since their work is in arithmetic progression:
First = x, Second = x + d, Third = x + 2d
Given:
10(x + 2d) = 14x
20d = 4x
d = x/5
Total work per day:
x + (x + d) + (x + 2d)
= 3x + 3d
= 3x + 3x/5
= 18x/5
They dug 324 m in 6 days, so per day work = 54 m.
18x/5 = 54
x = 15
The first digger digs 15 m per shift.
Q6. A man can complete a work in 20 days. With the help of a boy, the same work is completed in 12 days. If the total earning for the work is ₹500 and the amount is divided in proportion to the work done by each, what is the share of the boy?
Correct Option: C
Rationale:
Man’s rate = 1/20
Man + Boy rate = 1/12
Boy’s rate = 1/12 – 1/20
= 5/60 – 3/60
= 2/60
= 1/30
In 12 days:
Boy’s work = 12/30 = 2/5
Boy’s share = 2/5 × 500 = ₹200.
Q7. A man and a boy working together can complete a certain digging work in 40 days. Their rates of work are in the ratio 8:5. If the boy works alone, how many days will he take to complete the same work?
Correct Option: B
Rationale:
Man : Boy work rate = 8 : 5
Together rate = 13 units per day.
They complete work in 40 days.
Total work = 13 × 40 = 520 units
Boy’s rate = 5 units per day.
Time taken by boy alone = 520/5 = 104 days.
Q8. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days will one cow eat one bag of husk?
Correct Option: C
Rationale:
40 cows eat 40 bags in 40 days.
Total cow-days = 40 × 40 = 1600 cow-days
1600 cow-days are needed for 40 bags.
For 1 bag:
1600/40 = 40 cow-days
So one cow eats one bag in 40 days.
Q9. 8 men and 5 women working 6 hours a day can complete a work in 4 days. 4 men and 5 women working 8 hours a day can complete the same work in 5 days. 5 boys working 8 hours a day can complete the same work in 30 days. If 4 men, 3 women and 4 boys work together for 5 hours every day, in how many days will they complete the work?
Correct Option: A
Rationale:
Let one man’s hourly work = m, one woman’s hourly work = w, one boy’s hourly work = b.
From first condition:
(8m + 5w) × 6 × 4 = 1
8m + 5w = 1/24
From second condition:
(4m + 5w) × 8 × 5 = 1
4m + 5w = 1/40
Subtract:
4m = 1/24 – 1/40 = 1/60
m = 1/240
Then:
4m + 5w = 1/40
1/60 + 5w = 1/40
5w = 1/120
w = 1/600
From third condition:
5b × 8 × 30 = 1
b = 1/1200
Now rate of 4 men, 3 women and 4 boys:
4/240 + 3/600 + 4/1200
= 1/60 + 1/200 + 1/300
= 1/40 per hour
Working 5 hours per day:
Daily work = 5/40 = 1/8
Time = 8 days.
Q10. Using the same information above, if women and boys cannot be employed, what is the minimum number of men required to complete the work in 6 days if working hours per day cannot exceed 9?
Correct Option: B
Rationale:
From the previous solution:
One man’s hourly work = 1/240
Maximum working hours:
6 days × 9 hours = 54 hours
Work done by one man in 54 hours:
54/240 = 9/40
Number of men required:
1 ÷ 9/40 = 40/9 = 4.44
Minimum whole number of men = 5.
Q11. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same work in 2 days, the time taken by 15 men and 20 boys to do the same work will be:
Correct Option: B
Rationale:
Let one man’s daily work = m and one boy’s daily work = b.
6m + 8b = 1/10
26m + 48b = 1/2
Multiply first equation by 5:
30m + 40b = 1/2
Compare with:
26m + 48b = 1/2
Subtract:
4m – 8b = 0
m = 2b
Using 6m + 8b = 1/10:
6(2b) + 8b = 1/10
20b = 1/10
b = 1/200
m = 1/100
Rate of 15 men and 20 boys:
15/100 + 20/200
= 15/100 + 10/100
= 25/100 = 1/4
Time required = 4 days.
Mandays, Time and Work Questions for CET 2026 Quant Preparation
Mandays, Time and Work is a key arithmetic topic for CET 2026, MBA entrance exams, banking exams, aptitude tests and campus placement preparation. These questions test work rate, efficiency, combined work, individual capacity, wages, man-days, working hours and proportional productivity. A strong understanding of Time and Work helps students solve pipe and cistern, labour efficiency, project completion and wage distribution problems with speed and accuracy. In CET Quant, these problems often involve two workers, multiple workers, men-women-boys combinations, changing workforces and shared earnings. The best approach is to convert every person’s work into a unit rate and then apply total work equals rate multiplied by time. Regular practice improves fraction handling, equation formation and shortcut calculation. This quiz includes detailed step-by-step solutions so students can revise concepts, identify common traps and strengthen exam readiness. Use this Mandays, Time and Work practice module to improve calculation speed, accuracy and confidence for high-scoring CET 2026 Quant attempts.
