Today i overheard my daughter working out a
percentage problem as below:
"An oven costed 18000 last year but now costs 3300 less this year.
What's the percentage decrease in price?"
She was going for the formula and slightly confused as what to put in numerator what in denominator, and that happens even to adults.
So, i could not help but jump in, and try to break it down to her as below.
Some gyan to start off :)
Firstly, "per cent" means per 100.
And why do we talk in terms of "per cent"?
Imagine we have a farm where we grew 9789 mangoes 2 years before, 7989 last year and 9987 this year.
We just want a fair idea of how we are doing as farmers year on year.
Are we improving, regressing, or if we have regressed in the past, have we caught up now.
So a good measure would be:
For every 100 mangoes we grew last year, how many more (or less) have we grown this year?
When we stock the mangoes, lets stock them in bags of 100 and keep a count of those bags, lets say some 'N'.
When we harvest the next year, we divide our mangoes equally into the same 'N' number of bags.
The number of mangoes in the bag tells us how many more or less we grew this year compared to last year.
Coming back to the problem:
Last year price was 18000.
In 18000, how many 'cents'* do we have ?
180 right? (*just hope no US person reads this 😄 cent here refers to Latin centum i guess)
So we can break 18000 down as 180 rows of 100s:
1 100
2 100
3 100
.................
.................
178 100
179 100
180 100
Now the price reduced by 3300, and we need to find the so-called percent decrease right?😏
Let's imagine that the "percent" decrease is some X.
What does that mean? It means our 180 bags will look something like this:
1 100 - X
2 100 - X
3 100 - X
......................
......................
178 100 - X
179 100 - X
180 100 - X
How many Xs are there in total?
180
Great, and this 180*X should be equal to?
The reduction in price, 3300.
So X, the "percent" decrease is?
3300/180
Cool 😎
But, what if we cannot divide our mangoes into bags of 100 as in the gyan section?
In that case, lets represent each mango by 100 stones, and store the stones instead in groups of 100.
For 9789 mangoes, we get 9789 bags each carrying 100 stones.
Next year, we have 7989 mangoes, and thus 798900 stones, which is 180000 stones less.
Thus percent drop in stones would be (180000/9789) = 18.38
But since the ratio of mangoes to stones is always same (1:100), the above 18.38 reduction in 'per cent' of stones holds good for the reduction in 'per cent' of mangoes as well, correct?
😕
Well, think about it :-) ...
