Question

If $5^y–5^{(y-1)}=100$, then what is the value of $(3y{)}^y$?

• A. 256
• B. 343
• C. 216
• D. 729

Answer 1

The correct option is D 729

$5^y-\frac{5^y}{5}=100;5^y(1-\frac{1}{5})=5^2\times 4;5^y\left(\frac{4}{5}\right)=5^2\times 4$
$⟹5^{(y-1)}\times 4=5^2\times 4;y-1=2;y=3.$ Answer is $(3y{)}^y=(9{)}^3=729$.