udaymathapati wrote:
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
A. \(\frac{1}{(r+2)}\)
B. \(\frac{1}{2r+2}\)
C. \(\frac{1}{3r+2}\)
D. \(\frac{1}{r+3}\)
E. \(\frac{1}{2r+3}\)
Responding to a pm:
There is no 'best' way to solve a problem, in my opinion. The best way for you depends on what you are comfortable with. You can follow Bunuel's algebraic approach here (by taking x as the fraction of saving) or you can plug in values for r and check (or do something else... I would like to plug in values for r as shown in my second method)
Say r = 0
Whatever he saves this year, he has only that next year so he must save 1/3 this year (so that he spends 2/3 this year) Only options D and E give 1/3 when r = 0.
Say r = 1
Whatever he saves this year, it becomes double. This double should be half of what he spends this year. So what he spends this year should be 4 times what he saves i.e. he should save 1/5 of his income this year. Out of D and E, only E gives you 1/5
Answer E
OR, preferably, look for a value of r which gives a different answer for each option right in the beginning. I would choose r = 2.
Whatever he saves, it becomes 3 times. This 3 times amount must be half of what he spends this year. So what he spends this year must be 6 times of what he saves. Therefore, he saves 1/7 of his income. Only option E gives 1/7
_________________
Karishma Bansal - ANA PREP
*SUPER SUNDAYS!* - FREE Access to ALL Resources EVERY Sunday
REGISTER at ANA PREP
(Includes access to Study Modules, Concept Videos, Practice Questions and LIVE Classes)
YouTube Channel
youtube.com/karishma.anaprep