Percentage: The Magical A-B Rule & it's Applications ( Part 1 of 2)
In this Article you will learn:
The Magical A-B Rule and its application in following cases:
CASE 1: A’s income x% more than B, by how much percentage B’s income is less than A
CASE 2: A’s income x% less than B, by how much percentage B’s income is more than A
CASE 3: Problems related to Profit/Loss, Selling Price & Cost Price.
The Magical A-B Rule and its application in following cases:
CASE 1: A’s income x% more than B, by how much percentage B’s income is less than A
CASE 2: A’s income x% less than B, by how much percentage B’s income is more than A
CASE 3: Problems related to Profit/Loss, Selling Price & Cost Price.
CASE 4: When A X B = Constant (when product of two quantities is constant AB Rule can be applied)
Case 4.1: Price x Consumption= Expenditure (if Expenditure is constant AB Rule can be applied) e.g. When Price of sugar is increased/decreased by 20% by how much consumption should decrease/increase so that expenditure is constant.
CASE 4.2: For rectangle Length x Width = Area (if Area is constant AB Rule can be applied) e.g. If length of Rectangle is increased by 20%.By how much percentage width should decrease so that area of rectangle remains constant.
CASE 4.3: In Speed Time Distance (STD): Speed x Time = Distance (if Distance is constant AB Rule can be applied) e.g. Rohan takes 1 hour to reach his office from home. If he increases his speed by 25% how much time will he take to reach office from home?
After reading this article you will understand that all these problem can be solved using only one method i.e. A-B Rule. The benefit of A-B rule is that it is fastest method to solve above type question (many in 5 seconds- 10 second only).
I suggest you all to invest time in understanding this article, once you understand, above type questions will be fun for you.
To understand A-B Rule knowledge of Percentage to Fraction conversion is required. If you have not read my previous article on Percentage to Fraction conversion: Read it by clicking link below first and then come back.
The Magical A-B Rule
Let us start with Case 1 & Case 2 to understand A-B Rule: Case 1: A’s income is 25% more than B. By how much percentage B’s income is less than A’s Income.
Step 1: Identify the key word given in the question i.e. more than/ less than.
Step 2: Now we will make an A-B diagram based on given data. First write A and B leaving some space between them
Step 3: In above given Question A’s income is 25% more than B’s Income. It means if we increase B’s income by 25% we will get A’s income. (do not proceed until you understand this statement; take your time). Let us represent this in our diagram.
Note: Here + sign denotes an increase means when we move in Arrow direction & B’s income is increased by 25% we get A’s income.
Step 4: Now convert the Given Percentage to Fraction since we all know 25% = 1/4 and write it above blue arrow ( in solving problems you need not to make more than one diagram only one diagram will suffice)
Now we have represented the given data in our diagram.
Step 5: for finding the answer by how much % B’s income is less than A’s income.
Now we have to move from A to B lets draw it
Step 5: for finding the answer by how much % B’s income is less than A’s income.
Now we have to move from A to B lets draw it
Now in the above figure if we fill the? (Question Mark) we will get our Answer.
Step 6 : Getting The Answer
a) If sign of the fraction in blue arrow is + (positive means increase) then sign of the fraction in red arrow will be – (negative: means decrease).
Note: its common sense, Think if you have common sense, if you don’t have it ,do not worry just remember positive(+) becomes negative(-) and negative(-) becomes (+).
Note: its common sense, Think if you have common sense, if you don’t have it ,do not worry just remember positive(+) becomes negative(-) and negative(-) becomes (+).
b) Let us write fraction in red arrow, numerator of red arrow will be same as numerator of blue arrow.
Note: Always remember, while applying A-B Rule, Numerator does not Change
c) Denominator of red arrow = (denominator of blue arrow + numerator of blue arrow) i.e. 4+1=5 (I have added 4 and 1 since + was preceding the blue arrow fraction).
- If fraction above blue arrow has + symbol, denominator & numerator will be added.
- If fraction above blue arrow has - symbol, denominator & numerator will be subtracted.
Answer: Since we know -1/5 = -20%, so if A’s income is 25% more than B. Then B’s income is 20% less than A.
Case 2: A’s income is 25% less than B. By how much percentage B’s income is more than A’s Income.
Step 1: Identify the key word in given relation in the question; here it is less than/more than.
Step 2: Now we will make an A-B diagram based on given data. First write A and B leaving some space between them
Note: Here - sign denotes a decrease; it means if we move in Arrow direction & B’s income is decreased by 25% we get A’s income.
Step 4: Now convert the Given Percentage to Fraction since we all know 25% = 1/4 and write it above arrow ( in solving problems you need not to make more than one diagram only one diagram will suffice)
We have represented the given data in question in above diagram.
Step 5: for finding the answer by how much % B’s income is more than A’s income. we need to move from A to B lets draw it:
Now in the above figure if we fill the? (Question Mark) we will get our Answer.
Step 6: Getting the Answer
a) If sign of the fraction in blue arrow is – ( negative: means decrease) then sign of the fraction in red arrow will + ( positive: means increase)
Note: its common sense, Think ,if you have common sense, if you don’t have it,do not worry just remember positive(+) becomes negative(-) and negative(-) becomes (+).
b) Let us write fraction in red arrow, numerator of red arrow will be same as numerator of blue arrow.
Note: Always remember, while applying A-B Rule, Numerator does not Change
c) Denominator of red arrow = (denominator of blue arrow - numerator of blue arrow) i.e. 4-1=3 (I have subtracted 4 and 1 since - was preceding the blue arrow fraction).
- If fraction above blue arrow has - symbol, denominator & numerator will be subtracted.
- If fraction above blue arrow has + symbol, denominator & numerator will be added.
Answer: Since we know +1/3 = +33.33%, so if A’s income is 25% less than B. Then B’s income is 33.33% more than A.
Note: if you have understood above two cases you are done with A-B Rule. Now let us understand the process to do such question In 10 seconds.
Let us try some questions:
Question: If A’s salary is 10% more than B. By how much percentage B’s salary is less than A.
A] 10% B] 9.09% C] 11.11% D] None
Solution:
1. + becomes -
2. Numerator is not changed, i.e. 1 same as above fraction.
3. Denominator= 10+1=11
4. Answer= -1/11=-9.09% i.e. option B.
Question: If A’s salary is 40% more than B. By how much percentage B’s salary is less than A.
A] 28.56% B] 40% C] 66.66% D] None
Solution: Fraction Equivalent of 40% = 2/5.
1. + becomes -.
2. Numerator is not changed i.e. 2.
3. Denominator= 5+2=7
4. Answer= -2/7 = -28.56% i.e. B’s income is 28.56% less than A. option A.
Question: If A’s salary is 20% less than B. By how much percentage B’s salary is more than A.
A] 16.66% B] 20% C] 25% D] None
Solution: Fraction equivalent of 20%=1/5
Answer: +1/4 = +25% i.e. B’s salary is 25% more than A. Hence option C.
Question: If A’s salary is 40% less than B. By how much percentage B’s salary is more than A.
A] 28.56% B] 40% C] 66.66% D] None
Solution: Fraction Equivalent of 40% = 2/5
Answer= +2/3= +66.66% i.e. B’s salary is 66.66% more than A’s salary hence Option C.
Summary: If you remember Percentage to Fraction Conversion. These Questions can be solve quickly. Let us see what your thought process should be in examination.
Question: A’s income is 20% more than B by how much % B’s income is less than A.
A] 16.66% B] 20% C] 25% D] None
More than ====>+ 20% ====> +1/5 becomes -1/6 =====> -16.66% (less than)
It means if you understand above article there is no need draw even a diagram or write anything on paper. You can really do it in 5-10 seconds time. Option A is correct.
It means if you understand above article there is no need draw even a diagram or write anything on paper. You can really do it in 5-10 seconds time. Option A is correct.
Question 2: A’s income is 30% less than B. By how much % B’s salary is more than A.
Solution: less than ===> -30% ====> -3/10 becomes +3/7====> +42.84% (more than)
Note: This Magical A-B Rule has applicability in other topics too, Click on the link below to read it:
Mock Questions
Q1] A’s salary is 50% more than B. By how much percentage B’s salary is less than A?
A] 30%
B] 33.33%
C] 50%
D] 100%
Q2] A’s salary is 75% more than B. By how much percentage B’s salary is less than A?
A] 25%
B] 33.33%
C] 42.84%
D] 50%
E] 75%
Q3] A’s salary is 50% less than B. By how much percentage B’s salary is more than A?
A] 30%
B] 33.33%
C] 50%
D] 100%
Q4] A’s salary is 75% less than B. By how much percentage B’s salary is more than A?
A] 42.84%
B] 50%
C] 75%
D] 100%
E] 300%
Q4] A’s salary is 12.5% less than B. By how much percentage B’s salary is more than A?
A] 9.09%
B] 10.00%
C] 14.28%
D] 20%
E] 25%
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