Formula Technique 12 & 13
Formula Technique 12: Combination of Direct and Inverse Proportions
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Some times we face questions in which a comparison of more than two quantities or entities is to be considers. In other words one quantity is increasing with other and decreasing with other. Such questions are actually involving direct and indirect or inverse proportion at the same time.
To solve such questions first we arrange data and then put arrows in same direction for directly proportionate and put arrows in reverse directions for quantities which are inversely pro ported
We try to understand such a situation with the help of an example;
Example: Forty men work for six hours and finish work in thirty days. How long 25 men will take to finish the same work if they work for eight hours daily?
Here we can see that if we want work to be finished in more days then there should less number of men or they eithr should work for less hours. i-e days are inversely proportion to both number of men and working hours.
We arrange data as under:
So if we put arrows for days in upward direction then we will put arrows for men and hours in downward direction or vise versa.
The we wirte this data as;
i-e we put multiplication sign between same directed arrow terms and then put equal sign between this product and the inversely pro ported fraction. Now we can find the value of ‘x’ by taking 30 to the other side of equal sign, i-e ;
So,we found that they will finish work in 36 days.
Formula Technique 13: Calculation of Distance Traveled by a Moving Object
Let’s suppose rocket or any other moving object is moving with speed ‘v’ and it covers a distance ‘s’ in time ‘t’.
The formula for calculation of distance ‘s’ is ;
or simply we write;
Example: A car is moving with speed of sixty kilo meter per hour, how much distance it will cover in two hours?
t= 2 hrs
using above relation,
s= 60 x 2 = 120 kilometers
Here we ensure that all metrics are taken in same Si units.
So, we can aslo do this problem as;
v=60 x 1000 meters/3600 seconds= 16.66 m/s
t= 2 hours = 2 x 3600 seconds = 7200 sec
then again using relation
s= 16.66 x 7200 s= 12000 meters