Question

The price of an item is decreased by 50%, by what percentage should the price be now increased to bring it back to the original price?​

Answer 1

Answer:

$let \: the \: price \: of \: item = x$

Price decreased by 50%, therefore :-

$price \: of \: item = x - 50\%ofx$

$= x - \frac{50}{100} \: of \: x$

$= x - \frac{x}{2}$

$= \frac{2x - x}{2}$

$= \frac{x}{2}$

Now, According to the question:-

$\frac{x}{2} + x\% \: of \: \frac{x}{2} = x$

$\frac{x}{2} + \frac{x}{100} of \frac{x}{2} = x$

$\frac{x}{2} + \frac{ {x}^{2} }{200} = x$

$\frac{100x + {x}^{2} }{200} = x$

$100x + {x}^{2} = x \times 200$

${x}^{2} = 200x - 100x$

$x = \sqrt{100} = 10$

Therefore, % should be increased = 10%.