Time and Work - Shortcut with Examples

Today I am going to share basic technique used to solve Time and Work questions. I have already shared Time and work tricks here. Question - 4 men can do 2 units of work, working 5 hours a day in 24 days .In how many days will 6 men do 3 units of work, working 6 hours a day?

The method to solve such questions can be Direct and Indirect Variation.

Direct Variation

It means when you increase A, B also increases OR when you decrease A, B also decreases.

Indirect Variation

It means when you increase A, B decreases OR when you increase B, A decreases

Let us understand it in a better way:

• 14×1.5 or 14 ×  15/10=21
• 14×1  =14
• 14×0.5 or 14×  5/10=7

What do you observe in the above three cases?

• When you multiply 14 by a value greater than 1 , the answer comes more than 14.
• When you multiply 14 by a value equal to 1 , the answer remains the same .
• When you multiply 14 by a value less than 1 , the answer comes less than 14

OR you can also say that:

Condition 1:

If you want to increase a number, NUMERATOR   of the multiplying fraction should be greater than the DENOMINATOR.

Condition 2:

If you want to decrease a number, NUMERATOR   of the multiplying fraction should be less than the DENOMINATOR.

Now, let us move on to our question

Now follow these steps:

Step 1: Men and days

We can see from the above picture that the number of men have increased from 4 to 6 , which means days should be decreased. So to decrease the value (24) , we should  we should follow condition 2 which says :

If you want to decrease a number, NUMERATOR   of the multiplying fraction should be greater than the DENOMINATOR.

So now we have two values in the column of men i.e. 4 and 6 and to reduce the value of 24. We will write:

Step 2: work and days

work ∝days,

if you increase the work ,days increase and vice-versa

Now we have to increase the value of 24 as work has increased from 2 to 3. To reduce we will follow condition 2.

If you want to increase a number, NUMERATOR of the multiplying fraction should be greater than the DENOMINATOR.

we will write:

Step 3: Hours and Day

Here the hours have increased from 5 to 6. So we have to reduce the value of 24. We will follow condition 1.

So the required number of days = 20

Question - A is twice as efficient as B and thrice as efficient as C. B and C together take 44 days to complete a work . How long will A, B and C take to do the work?

A= 2B= 3C 

B+C = 44 days

A = 2B = 3C = 6 

Why 6? Because the LCM of coefficients of A, B and C is 6.

If A’s efficiency = 6

B’s efficiency = 6/2 = 3

C’s efficiency = 6/3 = 2

NOTE: Efficiency ∝  1/D which means if efficiency increases, days decrease and vice- versa

So here in this case, the efficiency has increased from 5 to 11, which in turn again reduce the number of day . Follow condition 2

Required number of days = 44×  5/11=20 days.

The method mentioned above is very useful to solve such questions. Please understand it very attentively.

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