If A's income is r% more than B's

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sohailmbaprep: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu Feb 23, 2012 11:18 pm

by sohailmbaprep » Fri Dec 21, 2012 11:24 pm

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

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Source: Beat The GMAT — Problem Solving | Fri Dec 21, 2012 11:24 pm

puneetkhurana2000: Master | Next Rank: 500 Posts; Posts: 131; Joined: Wed Nov 14, 2012 2:01 pmFollowed by: 2 members; Thanked: 39 times

by puneetkhurana2000 » Fri Dec 21, 2012 11:39 pm

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!!!

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sohailmbaprep: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu Feb 23, 2012 11:18 pm

by sohailmbaprep » Fri Dec 21, 2012 11:49 pm

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

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Dec 22, 2012 2:06 am

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.
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