Percentages in 3 Bases

Maths in clat is that catalyst which decides whether you get in the tier A college or not. Those 20 marks can change your whole life and are the easiest to get once you get your techniques. And no i am not addressing the math geeks but everyone of you out their wish to prove their salt and crack clat. What you need to do is first brush up your techniques and then learn some tricks which make maths sums a cake walk.

Base 1

So to get started with first lets learn something called the golden percentages something which you need to learn by heart ,

1/1 =100%

1/2 = 50%

1/3 = 33.33%

1/4 = 25%

1/5 = 20%

1/6 = 16.66%

1/7 = 14.2857%

1/8 = 12.5%

1/9 = 11.11%

1/10 = 10%

1/11 = 9.09%

1/12 = 8.33%

1/13 =7.69%

1/14 = 7.148%

1/15 = 6.67%

1/16 = 6.25%

Learn these ratios by heart before you proceed on to solving further sums. You also need to create a further table for rations like 2/5 , 3/5, 4/5 and then for fractions with other bases.

Some tips :

If you notice the table of 1/7 you will find that that the number .142857 remain the same and change depending upon the remainder, eg for 2/7 it goes like .285714 for 3/7 it goes like .428571 so as the numerator increases the decimals change in ascending order starting from the next highest number and then the whole sequence of numbers.

For the ratios with denominator 9 you will see that the sequences after the decimal point move in a certain pattern for 2/9 it is 22.22 for 3/9 it is 33.33 and so on.

For the ratios of 11 the numbers move in a pattern like for 2/11 it 18.18, 3/11 it is 27.27% that is the table of 9 taken twice with a decimal point in between them.

By using the following tricks working with percentage problems becomes a child’s play for all of us.

So while you are at it solve the following questions without looking at the table

1. 2/9
2. 5/8
3. 3/5
4. 9/11
5. 5/6
6. 4/7
7. 4/13
8. 7/12
9. 6/13
10. 5/14

Base 2

Now that we have mastered the techniques we need to move ahead the next level.

Here we will learn to solve some percentage of others. For example we need to find 20% of 135 what we need to do

First think of 20% as 1/ 5 then just multiply 135 by 1/5 and you get 27 which is the answer.

Another example is if we need to find 37.5% of 64 , now if we remember our tables well, we need to think of 37.5% as 3/8 and then if we multiply 64 by 3/8 we get the answer as 24.

Now if we need to find 36.36% of 143 we first need to convert it into 4/11 then when we multiply it by 143 we get 52 as the answer.

Now that we are at it lets solve a few questions:

1. 62.5% of 156
2. 33.33% of 216
3. 16.66% of 66
4. 15.38% of 247
5. 44.44% of 261
6. 28.57% of 343
7. 40% of 755
8. 12.5% of 144
9. 8.33% of 288
10. 37.5% of 324

One thing you need to remember while doing these sums is that you are not doing any scientific experiment over here it is enough if you get your answer in the vicinity of the answers as the choices given to you wont be extremely close, so relax and happy solving.

Base 3

Ok now moving on to the third and most important level. Before you move on to here you need to be through with the earlier formulae.

Now take a look at a problem if A is 25% more than B then what % is B less than A. The immediate answer would be 25% and then you fall in the trap. Over here if you see that if B was 100 then A being 25% more would be 125 now to find what % B is less than A you Have to take % using 125 as the base , while to find what % A more than B we use 100 as the base and hence lies the basic difference.

Now before you start getting all tensed and frustrated relax , there is a easy way to solve these sums.

Ok so to solve the above sums

1. We need to remember that 25% can be thought as ¼
2. Now as A is 25% more than B, i.e. 25/100+100 or we solve it as 1/4 +1=5/4, a simple way to remember this is add the denominator to the numerator.
3. Now we invert the number which gives us 4/5
4. Then we subtract it from 1, i.e. 1-4/5=1/5, or a simple way to remember is to subtract then Numerator from the Denominator,
5. Now if we remember 1/5 =20%

And that’s our answer if A is 25% more than B the B is 20% less than A. In 6 simple steps.

Now lets take another example, if A is 33.33% less than B then what % is a B more than A. Now to solve this question.

1. We convert 33.33% into its fraction form i.e. 1/3
2. Now we subtract the numerator from the denominator, i.e. 3-1/3, 2/3
3. Now we invert this, it gives us 3/2
4. Now we subtract 1 from this 3/2-1, or the denominator from the numerator, 3-2/2
5. This gives us 1/2 which is equal to 50%

Hence if A is 33.33% less than B then B is 50% more than A.

Now Solve the follow sums using the above explained method.

1. If A is 20% more than B then what % is B less than A
2. If A is 10% less than B , then what % is B more than A
3. If A is 12.5% more than B then what % is B less than A
4. If A is 16.67% less than B, then what % is B more than A
5. If A is 11.11% more than B , then what % is B less than A

So Happy Solving !!

Yashashree Mahajan.