Question

If 3 men and 4 women can finish the work in 24 days, 4 men and 8 women can finish the same work in 15
days, in how many days will it take for one man alone to finish the same work?
240 days
o 200 days
CO2
150 days
0 120 days​

Answer 1

Answer:

Option D : 120 days

Step-by-step explanation:

Given:

• 3 men and 4 women can complete a work in 24 days
• 4 men and 8 women can complete the work in 15 days

To Find:

• Days taken by one man alone to complete the work

Concept:

Create linear equations in two variables using the given data. Solving it by elimination method we get the value of the variables.

Solution:

Let work done by 1 man in one day = x

Let work done by 1 woman in one day = y

Hence by first case,

3 men and 4 women finish the work in 24 days

3x + 4y = 1/24--------(1)

Now by second case,

4 men and 8 women finish the work in 15 days

4x + 8y = 1/15--------(2)

Multiply equation 1 by 2

6x + 8y = 2/24

6x + 8y = 1/12 ------(3)

Solve equation 2 and 3 by elimination method,

6x + 8y = 1/12

4x + 8y = 1/15

2x = 1/12 - 1/15

2x = (15 - 12)/180

2x = 3/180

2x = 1/60

x = 1/120

Hence days taken by one man alone to complete the work = 120 days

Hence option D is correct.

Answer 2

Given :- If 3 men and 4 women can finish the work in 24 days, 4 men and 8 women can finish the same work in 15

days, in how many days will it take for one man alone to finish the same work ?

A) 240 days

B) 200 days

C) 150 days

D) 120 days

Solution :-

given that,

→ 3M + 4W can finish the work in = 24 days.

and,

→ 4M + 8W can finish the same work in = 15 days.

since work is same in both case , comparing work we get,

→ 24(3M + 4W) = 15(4M + 8W)

→ 72M + 96W = 60M + 120W

→ 72M - 60M = 120W - 96W

→ 12M = 24W

→ M/W = 24/12

→ M/W = 2/1

→ M : W = 2 : 1 .

So, Let Efficiency of each Men is 2 unit of work per day and Efficiency of each women is 1 unit of work per day.

Than,

→ Total work = 24(3M + 4W) = 24(3*2 + 4*1) = 24(6 + 4) = 24 * 10 = 240 units .

Or,

→ Total work = 15(4M + 8W) = 15(4*2 + 8*1) = 15(8 + 8) = 15 * 16 = 240 units.

Therefore,

→ Total work done by 1 man alone = (Total work) / (Efficiency of 1 man per day) = 240 / 2 = 120 days. (Option D) (Ans.)

Hence, 1 man alone can finish the same work in 120 days.

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