Problem Solving

1)If A's income is r% more than B's ,then B's income is less than that of A by how much % ??
2)If P is current population of a town ,what would be it's populatio after N years if the grows annually by r%

I have come across formulas for such problems but don't know how they derived them..i don't want to mug up the formula ,please let me know how to solve such problems

You can use some numbers.

1)If A's income is r% more than B's ,then B's income is less than that of A by how much % ?

Take A = 150, and r = 50% more than B = 100.

Then B's income is less than that of A by (150 - 100)/150 = 33.33%

2)If P is current population of a town ,what would be it's population after N years if it grows annually by r% ?

Take P = 100, r = 50% and N = 4 Years

P after 1 year = 100 + 100/2 = 150.
P after 2 years = 150 + 150/2 = 225.
P after 3 years = 225 + 225/2 = 337.5.
P after 4 years = 337.5 + 337.5/2 = 506.25.

Hope this explains!!!

puneetkhurana2000 wrote:You can use some numbers.

1)If A's income is r% more than B's ,then B's income is less than that of A by how much % ?

Take A = 150, and r = 50% more than B = 100.

Then B's income is less than that of A by (150 - 100)/150 = 33.33%

2)If P is current population of a town ,what would be it's population after N years if it grows annually by r% ?

Take P = 100, r = 50% and N = 4 Years

P after 1 year = 100 + 100/2 = 150.
P after 2 years = 150 + 150/2 = 225.
P after 3 years = 225 + 225/2 = 337.5.
P after 4 years = 337.5 + 337.5/2 = 506.25.

Hope this explains!!!

alright thnx, now what if the case reverses, i mean if i have to calculate population n years back and by how much B's income is more than A's

sohailmbaprep wrote:If A's income is r% more than B's ,then B's income is less than that of A by how much % ?

Approach 1:
Let B = 100.

Since A's income is r% more than B's income:
A = B + (r% of B) = 100 + (r/100)100 = 100+r.

Percent change from A to B = (A-B)/A * 100 = ( 100+r - 100 )/(100+r) * 100 = 100r/(100+r).

Approach 2:
Plug in a value for r.

It can be helpful to know the following:
A 25% INCREASE from X to Y is equal to a 20% DECREASE from Y to X.

Let r=25, implying that A's income is 25% MORE than B's income.
The result is that B's income is 20% LESS than A's income.
Now we plug r=25 into the answers to see which yields our target of 20%.

Answer choice: 100r/(100+r)
(100*25)/(100+25) = 20.
Success!