MDH MCQ Quiz - Objective Question with Answer for MDH - Download Free PDF

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.

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.

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.

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.

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.

Given:

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

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.

Given:

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.

Given:

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.

Given:

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.

Given:

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.

Given:

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.

Given:

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. 

Given:

(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.  

Given:

30 men can complete a work = 12 days

Formula used:

Total work = efficiency × time

Calculation:

Let, the efficiency of a man = M

According to the question:

⇒ (30 × M × 6) + (54 × M × D) = 30 × M × 12

⇒ (54 × M × D) = 30 × M × 6

⇒ D = (30 × 6)/54 = 10/3 

⇒ D = 3\(\frac{1}{3}\) days

∴ The correct answer is 3\(\frac{1}{3}\) days.