 Well, interesting variation to percentage problems is ratios to percentage problems. And in such problems usually we find problems like these. So, let us say there is a school and in school the problem goes like this. The ratio of girls to boys is 3 is to 5 and then they ask what is the percentage of girls in the school. Now, usually students make some mistake in this problem. Assuming that they know the concept of percentage, they know they have to take some quantity in the numerator and some quantity in the denominator. And all they do is look at these two values. Because this ratio converts to 3 by 5, they go ahead and try to convert this into percentage. They find the answer. But remember this is girls in numerator but in the denominator this is still boys. In denominator we don't need number of boys but we need the total number of students. When we are talking about percentage of girls in school, we are talking about percentage of girls among all the students. All the students comprise of boys as well as girls again. So, this ratio is wrong. A better way to deal with this problem is to look at the number of girls and write it as 3y. There is some constant. So, this is number of girls and then we will write 5y, y is a constant that multiplies the ratio. Why could be anything? It could be 100 or it could be 200, it could be 50. So it just assumes certain number of girls and certain number of boys and then therefore the total number of students is addition of these two which is 8y and now we can go ahead and solve the percentage. So the number of girls is 3y and the total is 8y. So this is basically girls divided by total number of students. And now we can convert this into some percentage by keeping the denominator as 100 and let's keep the variable as g for the percentage of girls. This gives us 3 by 8 to be equal to g by 100 because we can cancel out y because that was just a multiplying constant and to find g we can cross multiply. So 100 times 3 is equal to 8 times g. Therefore g is equal to 100 times 3 divided by 8 and therefore g becomes 37.5 percent and this is how we found the percentage of girls when the ratio of girls to boys was given to us. It's all another problem. Now here goes another problem to make a recipe item A, item B and item C should be mixed in the ratio 3 is to 5 is to 8. What percentage of each item is there in the final product? I am not good at cooking so I couldn't write a good recipe so I just assumed some recipe and chose 3 items sorry about that. But now what we need is the final product percentage composition of each item. So we know that item A is to B is to C is 3 is to 5 is to 8. Now percentage of item A can be given by the parts of item A which is 3 divided by the total parts. Total parts simply will mean some 3 y plus 5 y plus 8 y and if we are writing y we would also write y for item A and this gives me 16 y we just write 16 y or this is simply 3 by 16. So you just simply have to add up all the values in the ratio and to find the percentage of it. Let's just write percentage of A I'll just write variable A divided by 100 16 parts which are total parts correspond to 100 percent so what is 3 out of 16? This gives me A is equal to 300 divided by 16 after cross multiplication and this is equal to 18.75 and therefore percentage of A in final product is 18.75. Now similarly we can find parts of B. Now parts of B are 5 y or basically 5 by 16 so now percentage of B can be given by 5 y by 16 y which is 5 by 16 and then we just equate it to B by 100 and this gives me B is equal to 500 divided by 16 and that gives me 31.25 and therefore percentage of B in final product is 31.25. Now what about C? We can simply write percentage of C as 8 y divided by 16 y and that gives me 8 by 16 which is 1 by 2 and equating it to some C by 100 I can find C after cross multiplication C is equal to 100 divided by 2 which is 50. So percentage of product item C in the final product is 50 percent and this is how we can solve problems related to ratio to percentage conversion.