Question

the price of an iteam increased by 25%.If the price of the item after the increase is $2,find the original price​

Answer 1

Let Original Price of Item=$x

$When \:\ x \:increased \\by\: 25\%\: it \:become=\ x$

so,

$x + (x \times 25\%) = 2 \\ \\ x + (x \times \frac{\cancel{25}}{\cancel{100}} ) = 2 \\ \\ x + \frac{x}{4} = 2 \\ \\ \frac{4x + x} {4} = 2 \: \: \: \: (lcm = 2) \\ \\ \frac{5x}{4} = 2 \\ \\ x = \cancel2 \times \frac{4}{\cancel5} \\ \\ x = 0.4 \times 4 \\ \\ x = 1.6$

Original Price=$1.6

Check

$1.6 + (1.6 \times 25\%) \\ \\ 1.6 + \frac{1.6}{4} \\ \\ \frac{1.6 \times 4 + 1.6}{4} \\ \\ \frac{6.4 + 1.6}{4} \\ \\ = \frac{8}{4} \\ \\ = 2$

Hence Proved.

$\boxed{\mathbf{\large{Original\:Price=\ 1.6}}}$

Answer 2

Answer:

$ 1.60.............................