Question 1201145

Adam’s annual salary is RM120,000 and his total expenses is RM90,000. 

His salary increases by RM12,000 each year while his expenses increase by RM15,000 each year.
Represent his total savings as series.

 (120000-90000)+(144000-105000)+(156000-120000)....
(120000+144000+156000)... -(90000+105000+120000)...
Let n be the number of years when income = expenses
Both are arthimatic sequences
Tn= a+(n-1)d
a=120000
d =12000
tn= 120000 +(n-1)12000
=  108000 +12000n

Expense after n years
Tn= 90000+(n-1)15000
= 75000+15000n

Income = expense

108000 +12000n=75000+15000n

3000n =33000
n=11    Eleventh year there is no saving

Let x be the expence increase every year
number of years = 25 when saving is nil
T25= 120000 +(25-1)12000
= 120000 +288000
= 408000

408000 = 90000 +(25-1)x
408000  -  90000=24x

318000=24x

x= 13250 expence increase every year