Buying Apartments
As of January, the price of an apartment in Patuli, a small town in India, is 25 Lakhs. But the price rises by 1 Lakh every year. Chandan currently has 4 Lakhs in his bank account and earns 5 Lakhs every month.
By what time, if ever, will he be able to afford an apartment in Patuli?
Note:
One Lakh (rupees) equals 100,000 (rupees) in Indian numbering system.
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1 solution
If m denotes the month of the year, then the cost of the appartment is:
Q = 2 5 + 1 2 1 m
since the initial value is 25 Lakhs and every 12 months (a year) the cost of the appartment is raised by 1 Lakh.
The money that Chandan has are:
M = 4 + 5 ( m − 1 )
Since in the first month (January (m=1)) he has 4 Lakhs and each month he gains 5 Lakhs.
Chandan will be able to afford the appartment when:
M = Q ⇒ 4 + 5 m − 5 = 2 5 + 1 2 m ⇒ . . . ⇒ m ≈ 5 . 2 8
So, Chandan will be able to afford the appartment during May, which is before September.