MDH MCQ Quiz - Objective Question with Answer for MDH - Download Free PDF
Last updated on Jun 6, 2025
Latest MDH MCQ Objective Questions
MDH Question 1:
A group of 5 men or 12 women can complete a particular task in 78 days. How long will it take for 5 men and 12 women working together to finish the same task?
Answer (Detailed Solution Below)
MDH Question 1 Detailed Solution
Given:
5 men can complete a task in 78 days.
12 women can complete the same task in 78 days.
Formula used:
If M1 persons can do a work in D1 days, and M2 persons can do the same work in D2 days, then M1D1 = M2D2.
Also, Work = Efficiency × Time
Calculations:
5 men ≡ 12 women
5 men and 12 women:
Total equivalent men = 5 men (from the group of men) + 5 men (equivalent to 12 women)
⇒ Total equivalent men = 10 men
We know that 5 men can complete the task in 78 days.
Let D be the number of days 10 men will take.
Using the formula M1D1 = M2D2:
5 × 78 = 10 × D
⇒ D = (5 × 78) / 10
⇒ D = 78 / 2
⇒ D = 39 days
∴ It will take 39 days for 5 men and 12 women working together to finish the same task.
MDH Question 2:
8 men and 3 women can do a piece of work in 7 days, whereas 5 men and 1 woman can do it in 12 days. How many men should assist 8 women so that the same work is completed in \(4\frac{1}{5}\) days ?
Answer (Detailed Solution Below)
MDH Question 2 Detailed Solution
Given:
8 men and 3 women can complete a work in 7 days.
5 men and 1 woman can complete the same work in 12 days.
We need to find how many men should assist 8 women to complete the work in 4 and 1/5 days (which is 21/5 days).
Formula used:
Work = (Number of Men × Days × Hours) / Work Done (assuming efficiency of all workers is constant and work done is 1 unit).
In cases involving different types of workers (men and women), we first find the relationship between their efficiencies.
Total Work = (M1 × D1) = (M2 × D2) (where M represents man-days or man-equivalent-days)
Calculation:
Let 'm' be the efficiency of 1 man (work done by 1 man in 1 day).
Let 'w' be the efficiency of 1 woman (work done by 1 woman in 1 day).
From the first condition:
(8m + 3w) × 7 = Total Work ......(Equation 1)
From the second condition:
(5m + 1w) × 12 = Total Work ......(Equation 2)
Equating Equation 1 and Equation 2 to find the relationship between 'm' and 'w':
7(8m + 3w) = 12(5m + w)
⇒ 56m + 21w = 60m + 12w
⇒ 21w - 12w = 60m - 56m
⇒ 9w = 4m
⇒ m/w = 9/4
This means 1 man's efficiency is equivalent to 9/4 times a woman's efficiency, or 4 men do the same work as 9 women.
Now, let's find the total work using either equation. Using Equation 2:
Total Work = (5m + w) × 12
Substitute m = (9/4)w into the Total Work equation:
Total Work = (5 × (9/4)w + w) × 12
⇒ Total Work = 49w × 3 = 147w (units of work)
Now, let 'x' be the number of men required to assist 8 women to complete the work in 4 and 1/5 days (21/5 days).
(x men + 8 women) × (21/5 days) = Total Work
(xm + 8w) × (21/5) = 147w
Substitute m = (9/4)w:
(x × (9/4)w + 8w) × (21/5) = 147w
(9x/4 + 8) × (21/5) = 147
9x/4 + 8 = 147 × (5/21)
⇒ 9x/4 + 8 = 7 × 5
⇒ 9x/4 = 35 - 8
⇒ 9x/4 = 27
⇒ x = 12
∴ The correct answer is option 3.
MDH Question 3:
A work can be completed by 8 men or 12 women in 25 days. 10 men and 5 women willcomplete the same work in
Answer (Detailed Solution Below)
MDH Question 3 Detailed Solution
Given:
8 men can complete the work in 25 days.
12 women can complete the same work in 25 days.
Formula Used:
M1 × D1 = M2 × D2 (when work is constant)
Let the work done by 1 man in 1 day be 'm' units.
Let the work done by 1 woman in 1 day be 'w' units.
Total work = Number of men × work per man per day × Number of days
Total work = Number of women × work per woman per day × Number of days
Calculation:
Work done by 8 men in 25 days = 8m × 25 = 200m units
Work done by 12 women in 25 days = 12w × 25 = 300w units
Since the work is the same:
200m = 300w
⇒ 2m = 3w
⇒ w = (2/3)m
Work of 5 women = 5 × w = 5 × (2/3)m = (10/3)m
So, 10 men and 5 women are equivalent to 10m + (10/3)m men.
Equivalent men = (30/3)m + (10/3)m = (40/3)m
Let the number of days taken by 10 men and 5 women be 'D' days.
Using the MDH formula:
M1 × D1 = M2 × D2
Here, M1 = 8 men, D1 = 25 days
M2 = (40/3) equivalent men, D2 = D days
8 × 25 = (40/3) × D
200 = (40/3) × D
600 = 40 × D
D = 600 / 40
D = 15
∴ 10 men and 5 women will complete the same work in 15 days.
MDH Question 4:
2 women and 5 men can together finish a work in 4 days while 3 women and 6 men can finish the same work in 3 days. Find the time taken by 1 man alone to finish the work.
Answer (Detailed Solution Below)
MDH Question 4 Detailed Solution
Given:
2 women + 5 men finish a work in 4 days.
3 women + 6 men finish the same work in 3 days.
Formula Used:
M1 × D1 = M2 × D2 (when work is constant, considering equivalent work units)
Let the work done by 1 man in 1 day be 'm' units.
Let the work done by 1 woman in 1 day be 'w' units.
Total work = (Number of women × work per woman per day + Number of men × work per man per day) × Number of days
Calculation:
Total work = (2w + 5m) × 4
⇒ 8w + 20m = Total Work (Equation 1)
Total work = (3w + 6m) × 3
⇒ 9w + 18m = Total Work (Equation 2)
Equating Equation 1 and Equation 2 (since the total work is the same):
8w + 20m = 9w + 18m
⇒ 20m - 18m = 9w - 8w
⇒ 2m = w
This means 1 woman does the same amount of work as 2 men in a day.
Substitute w = 2m into Equation 1 to find the total work in terms of 'm':
Total Work = 8(2m) + 20m
⇒ Total Work = 16m + 20m
⇒ Total Work = 36m units
The total work is 36 times the work done by one man in one day.
To find the time taken by 1 man alone to finish the work, we divide the total work by the work done by 1 man in a day:
Time taken by 1 man = Total Work / Work done by 1 man per day
Time taken by 1 man = 36m / m
Time taken by 1 man = 36 days
∴ 1 man alone will take 36 days to finish the work.
MDH Question 5:
39 persons can repair a road in 12 days , working 5 hours a day . In how many days will 30 persons , working 6 hours a day , complete the work?
Answer (Detailed Solution Below)
MDH Question 5 Detailed Solution
Given:
39 persons can repair a road in 12 days, working 5 hours a day.
Formula Used:
Work = Number of persons × Number of days × Number of hours per day
Calculation:
Work done by 39 persons in 12 days, working 5 hours a day:
Work = 39 × 12 × 5
Work = 2340
Let the number of days required for 30 persons working 6 hours a day be D.
Work = 30 × D × 6
Since the total work is the same, we equate the two expressions for work:
⇒ 39 × 12 × 5 = 30 × D × 6
⇒ 2340 = 180D
⇒ D = 2340 / 180
⇒ D = 13
∴ The correct answer is option 2.
Top MDH MCQ Objective Questions
A man and a woman can finish a work together in half the time taken by a woman and a boy together. A boy can finish the work alone in 20 days and 2 women together can finish it in 30 days. In how many days will the work be finished by 4 men?
Answer (Detailed Solution Below)
MDH Question 6 Detailed Solution
Download Solution PDFGiven:
Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)
A boy alone can finish the work = 20 days
2 women can finish the work = 30 days.
Concept used:
If total work is constant then,
Time ∝ (1/efficiency)
Formula used:
Total work = efficiency × time
Calculation:
2 women can finish the work = 30 days.
1 woman can finish the work = 30 × 2 = 60 days
Efficiency | Person | Time | Total work |
1 | Woman | 60 | 60 |
3 | Boy | 20 |
Now,
Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)
Time taken by (man + woman) : Time taken by (woman + boy) = 1 : 2
Efficiency of (man + woman) : Efficiency of (woman + boy) = 2 : 1
(Woman + boy) = (3 + 1) = 4
⇒ 1 unit = 4 units/day
⇒ 2 units = 4 × 2 = 8 units/day
Efficiency of (man + woman) = 8
Efficiency of man = 8 - 1 = 7 units/day
Time taken to complete the work by 4 men = 60/(4 × 7)
⇒ 60/28 = 15/7 = 2.14 days
∴ The correct answer is 2.14 days.
A group of men decided to do a job in 11 days but 16 men left the work after each day. The work, as a result, got completed in 15 days. How many men were there initially in the group?
Answer (Detailed Solution Below)
MDH Question 7 Detailed Solution
Download Solution PDFGiven:
A group of men decided to do a job in 11 day, but 16 men dropped out every day.
The job was completed in 15 days.
Concept used:
Total work = Efficiency of each worker × Number of days to finish × Number of total workers
Calculation:
Let there be Q men initially with the efficiency of 1 unit per day.
Total work = Q × 1 × 11 = 11Q units
According to the question,
Q + (Q - 16) + (Q - 16 × 2) + .... + (Q - 16 × 14) = 11Q
⇒ 15Q - (16 + 32 + .... + 224) = 11Q
⇒ 4Q = 16 × 105
⇒ Q = 420
∴ There were 420 men initially.
Working 5 hours a day, A can complete a task in 8 days and working 6 hours a day, B can finish the same task in 10 days. Working 8 hours a day, they can jointly complete the task in __________.
Answer (Detailed Solution Below)
MDH Question 8 Detailed Solution
Download Solution PDFGiven:
A working hours = 5 hours/day
A can complete a task = 8 days
B working hours = 6 hours/day
B can finish the same task = 10 days
Concept used:
M1 × D1 × H1 = M2 × D2 × H2
M = person ; D = days ; H = hours
Calculation:
According to the question:
⇒ A × 5 × 8 = B × 6 × 10
⇒ A/B = 3/2
Total work = A × 5 × 8 = 3 × 40 = 120 units
Required time taken = 120/{(3 + 2) × 8}
⇒ 120/40 = 3 days
∴ The correct answer is 3 days.
A group of men decided to do a job in 6 days, but 18 men dropped out every day. If the job was completed in 8 days, then how many men initially decided to do the job.
Answer (Detailed Solution Below)
MDH Question 9 Detailed Solution
Download Solution PDFGiven:
A group of men decided to do a job in 6 days, but 18 men dropped out every day.
The job was completed in 8 days.
Concept used:
Total work = Efficiency of each worker × Number of days to finish × Number of total workers
Calculation:
Let there be Q men initially with the efficiency of 1 unit per day.
Total work = Q × 1 × 6 = 6Q units
According to the question,
Q + (Q - 18) + (Q - 18 × 2) + .... + (Q - 18 × 7) = 6Q
⇒ 8Q - (18 + 36 + .... + 126) = 6Q
⇒ 2Q = 504
⇒ Q = 252
∴ There were 252 men initially.
A man, a woman and a boy can complete a job in 3, 5 and 15 days, respectively. How many boys must assist 1 man and 1 woman to complete the job in \(\frac{1}{5}\) of a day?
Answer (Detailed Solution Below)
MDH Question 10 Detailed Solution
Download Solution PDFMan's 1-day work = 1/3
Woman's 1-day work = 1/5
Boy's 1-day work = 1/15
According to the question-
⇒ 1 × (1/3) + 1 × (1/5) + x × (1/15) = 1/(1/5)
{ ∵ x be the no. of boys needed}
⇒ x/15 = 5 - (1/3) - (1/5)
⇒ x/15 = (75 - 5 - 3)/15
⇒ x = 67
∴ 67 Boys are needed to complete the work.
15 men can complete a work in 25 days, and 25 women can complete the same work in 40 days. If all 15 men and 25 women work together, in how many days will the work get completed?
Answer (Detailed Solution Below)
MDH Question 11 Detailed Solution
Download Solution PDFGiven:
15 men can complete a work = 25 days
25 women can complete the same work = 40 days
Formula used:
Total work = efficiency × time
Calculation:
Let the efficiency of a man = M
The efficiency of a woman = W
According to the question:
⇒ 15 × M × 25 = 25 × W × 40
⇒ M/W = 40/15 = 8/3
Total work = efficiency × time
⇒ 25 × 3 × 40 = 3000
Time taken to complete the work if 15 men and 25 women work together
⇒ 3000/{(15 × 8) + (25 × 3)} = 3000/(120 + 75)
⇒ 3000/195 = \(15 \frac{5}{13}\) days
∴ The correct answer is \(15 \frac{5}{13}\) days.
A group of college students had decided to complete a project in 10 days. As 2 students dropped out every day, the project got completed at the end of the 15th day. The number of students at the beginning of the project was:
Answer (Detailed Solution Below)
MDH Question 12 Detailed Solution
Download Solution PDFGiven:
A group of college students complete a project = 10 days
Formula used:
Total work = efficiency × time
Sum of n terms = (n/2) × [a + l]
Where, n = number of terms; a = first term; l = last term
Calculation:
Let the number of students in a group initially = x
According to the question:
⇒ x + (x - 2)......(x - 28) = x × 10
⇒ (15/2) × [x + x - 28] = 10x
⇒ 3 × [2x - 28] = 4x
⇒ 6x - 84 = 4x
⇒ 2x = 84
⇒ x = 42 students
∴ The correct answer is 42 students.
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 25 women complete it?
Answer (Detailed Solution Below)
MDH Question 13 Detailed Solution
Download Solution PDFGiven:
(4 men + 6 women) can complete a work = 8 days
(3 men + 7 women) can complete a work = 10 days
Formula used:
Total work = efficiency × time
Calculation:
⇒ (4 men + 6 women) × 8 = (3 men + 7 women) × 10
⇒ 2 men = 22 women
⇒ Men/women = 11/1
Total work = (3 men + 7 women) × 10
⇒ {(3 × 11) + (7 × 1)} × 10
⇒ (33 + 7) × 10 = 400
Time taken by 25 women to complete the work = 400/25 = 16 days
∴ The correct answer is 16 days.
A group of men decided to do a job in 13 days but 9 men left the work after each day. The work, as a result, got completed in 16 days. How many men were initially in the group?
Answer (Detailed Solution Below)
MDH Question 14 Detailed Solution
Download Solution PDFGiven:
A group of men decided to do a job in 13 days.
Formula used:
Total work = efficiency × time
Sum of n terms = n/2 × [a + l]
Where, n = number of terms;
a = first term; l = last term
Calculation:
Let the number of person in group initially = x
9 men left work after each day.
So it becomes an A.P series.
⇒ x + (x -9) + (x - 18)............ (x - 135) = x × 13
⇒ (16/2) × [x + x - 135] = 13x
⇒ 8 × [2x - 135] = 13x
⇒ 16x - (135 × 8) = 13x
⇒ 16x - 13x = 135 × 8
⇒ x = (135 × 8)/3 = 45 × 8 = 360 persons.
∴ The correct answer is 360 persons.
10 men can do a work in 25 days. After 12 days of work, 3 more men were engaged to finish the work. The number of days required to complete the remaining work is:
Answer (Detailed Solution Below)
MDH Question 15 Detailed Solution
Download Solution PDFGiven:
10 men can do work = 25 days
Formula used:
Total work = efficiency × time
Calculation:
Let the efficiency of a man = M
According to the question:
⇒ 10 M × 25 = 10 M × 12 + 13 M × D
⇒ 250 M - 120 M = 13 M × D
⇒ 13 M × D = 130 M
⇒ D = 130/13 = 10 days
∴ The correct answer is 10 days.