Shortcut methods/tricks in
*Percentage concept:
Important Points to Note:
1.When any value increases by
1.10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)
2.20%, it becomes 1.2 times of itself.
3.36%, it becomes 1.36 times of itself.
4.4%, it becomes 1.04 times of itself.
Thus we can see the effects on the values due to various percentage increases.
2.When any value decreases by
1.10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)
2.20%, it becomes 0.8 times of itself
3.36%, it becomes 0.64 times of itself
4.4%, it becomes 0.96 times of itself.
Thus we can see the effects on a value due to various percentage decreases.
Note:
1. When a value is multiplied by a decimal more than 1 it will be increased and when multiplied by less than 1 it will be decreased.
2. The percentage increase or decrease depends on the decimal multiplied.
Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and so on.
*Time and Distance problems:
1.Average Speed=Total distance/Total time
When they are more than one average speed then in order to find the average speeds of all here are some conditions
1.When time is constant Average speed is Average of all speeds.
2.When distance is constant then average speed is Harmonic mean of all average speeds.
For e.g: Two speeds s1,s2 Average speed=2/((1/s1)+(1/s2))
*Train Problems:
A train of length ‘l’ speed ‘s’ crossing a pole(man) of negligible length then time taken by train to train is
T=l/s
A train of length ‘l’ and speed ‘s’ crossing a platform of length ‘lp’, then time taken by train to cross platform is
T=(l+lp)/s
Relative speed Problems:
In solving Relative speed problems there arises two cases
Case 1: When two objects of speeds s1, s2 are moving in the same direction then relative speed is difference of their speeds (i.e., s1~s2)
Case 2: When two objects of speeds s1, s2 are moving in the opposite direction then relative speed is sum of their speeds (i.e., s1+s2)
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