Question

96 men are engaged for a project of constructing a railway track of length 18 km in four weeks.after one week it was observed that the work of 4 km was completed.how many additional men should be engaged for timely completion of project​

Answer 1

Given :- 96 men are engaged for a project of constructing a railway track of length 18 km in four weeks. after one week it was observed that the work of 4 km was completed.how many additional men should be engaged for timely completion of project ?

Solution :-

Given that, in one week 4km of railway track was completed by 96 men.

So,

• Time left now = 4 - 1 = 3 weeks.
• Work left = 18 - 4 = 14km of railway track.

Let us assume that, x men completes the rest work in rest time.

we know that,

• work done ∝ (1/Time) .

Applying chain rule now , we get,

→ M1 * D1 * W2 = M2 * D2 * W1

→ 96 * 1 * 14 = x * 3 * 4

→ 12x = 96 * 14

dividing both sides by 12,

→ x = 8 * 14

→ x = 112 men.

Therefore,

→ Additional men = 112 - 96 = 16 (Ans.)

Hence, 16 additional men should be engaged for timely completion of project.

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Answer 2

SOLUTION

GIVEN

• 96 men are engaged for a project of constructing a railway track of length 18 km in four weeks.
• After one week it was observed that the work of 4 km was completed.

TO DETERMINE

The number of additional men should be engaged for timely completion of project

EVALUATION

Here it is given that 96 men are engaged for a project of constructing a railway track of length 18 km in four weeks.

After one week it was observed that the work of 4 km was completed.

So in order to complete the project timely the target is :

To finish the project of constructing a railway track of remaining length of ( 18-4) = 14 km in remaining (4-1) = 3 weeks.

Now we have to determine the additional number of men required to complete the project timely

SOLVE USING RULES OF THREE

$\sf{}Length \: of \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Time \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Number$

$\sf{}track \: (km) \: \: \: \: \: \: \: \: \: \: \: \: \: \: (weeks) \: \: \: \: \: \: \: \: \: \: \: \: \: of \: men$

$\sf{} 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: 96$

$\sf{}14 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: ?$

Here length of the track and number of men is in direct proportion

Also time is in inverse proportion with Number of men

So by the Rules of three the number of men required

$\displaystyle \sf{} = 96 \times \frac{1}{3} \times \frac{14}{4}$

$\sf{} = 112$

Hence the additional number of men required

= 112 - 96

= 16

FINAL RESULT

The number of additional men should be engaged for timely completion of

Project is 16

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