A principal amount increases by \(\cfrac{1}{8}\) of itself every year. If it becomes 900 rupees in 7 years, then what was the initial principal amount?

Q.A principal amount increases by \(\cfrac{1}{8}\) of itself every year. If it becomes 900 rupees in 7 years, then what was the initial principal amount? (a) ₹ 400 (b) ₹ 600 (c) ₹ 800 (d) ₹ 480

Answer: D

Let’s assume the principal amount \((p)=x\) rupees
\(\therefore\) Total interest for 7 years = \(x\times \cfrac{1}{8}\times 7 \) rupees
\(=\cfrac{7x}{8}\) rupees
\(\therefore\) According to the given condition, \(x+\cfrac{7x}{8}=900\)
or, \(\cfrac{8x+7x}{8}=900\)
or, \(\cfrac{15x}{8}=900\)
or, \(x=900\times \cfrac{8}{15}=480\) rupees