Joyful Maths: SPICY TREAT for Time and work problems

Sandeep Tripathi

All school-level students and  graduates preparing for various competitive examinations  encounter problems in math like the soup of  men, days, hours & work, simply put, time and work problems . I remember how much I dreaded them even after my college days for the fear of not solving them at 100% confidence level. 

Today we shall give them a special treatment, a spicy treat as these questions are asked up to High School and even in higher level competitive examinations.

Now let’s have a look at this commonly asked sample problem, though a bit towards the tougher side:

12 men working 8 hours a day for 5 days complete a wall 2 m high 40 m long and 30 cm thick. If 15 men are employed at the rate of 6 hours a day to complete a similar wall 1.5 m high 30 m long and 40 cm thick then in how many days will the work be completed?

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Such a lengthy problem! ….. but don’t worry you will have the answer in a few seconds after a little practice of  adding the correct spices.

LEARNING THE TECHNIQUE

This should take a normal read of a few minutes. Be slow and patient while you sharpen your tools.

Spice used is: “MDH Masale”.

Note: M of masale will be  inverted to W and put in the bottom line.  Keep MDH same for both cases. 

And now the single line mental solution is

12x5x8      = 15xDx6       

2x40x0.30    1.5x30x0.40

Cancelling the common terms we get the number of days, D =8 

For practice now try this

If 10 children each working for 4 hours a day can complete a project in 6 days then working for how many hours a day will 8 children complete a similar work in 15 days?

Check your answer: 2 days

In this case, we just have 2 things, children for men, M and the hours, H. The same formula can be used again, with more ease as now,   MH case 1 = MH case 2.

(instead of using all of MDHW)

So, this formula gives you all liberty and flexibility of use.

Keep pacticing and within no time you will be able to solve such problems by yourself in one or two lines in a short time of few seconds or a minute.

Happy solving !

The writer is Lecturer (Physics), Govt. Sr. Sec. School, Sector-7, Panchkula