Question

The marked price of a toy is same as the percentage of GST that is charged. The price of the toy is ₹ 24 including GST. Taking the marked price as x, form an equation and solve it to find x.

Answer 1

Given: The marked price of the toy = x in ₹ and this same number x is the GST rate in percent. The price including GST is ₹ 24.

Step-wise calculation:

1. GST amount

= x% of marked price 

= `x/100 xx x`

= `x^2/100`

2. Price including GST

= Marked price + GST 

= `x + x^2/100`

= 24

3. Multiply by 100:

100x + x² = 2400

4. Rearranged quadratic:

x² + 100x – 2400 = 0

5. Discriminant Δ

= 100² – 4 × 1 × (–2400) 

= 10000 + 9600

= 19600

6. `sqrt(Δ) = 140`.

Solutions: `x = (-100 ± 140)/2`.

`x = (-100 + 140)/2`

= `40/2`

= 20   ...(Acceptable, Positive)

`x = (-100 - 140)/2`

= `(-240)/2`

= –120   ...(Reject, Negative rate not allowed).

Marked price x = ₹ 20. 

Thus, GST = 20% and GST amount = 20% of 20 = ₹4, so total = 20 + 4 = ₹ 24.