For any purchase of less than $1000, a person doesnt need to pay any

Solution

• We are given three cases,

o Case 1: If the purchase value < $1000, then no need to pay tax
o Case 2: If the purchase value is between $1000 and $2000, then the tax = 5% of the excess value over $1000
o Case 3: If the purchase value > $2000, then the tax = 5% of ($2000 – $1000) + 10% of the excess value over $2000.

• Possible purchase value, such that the total tax paid ≤ 4% of the total purchase value

• So, if we observe, all the options given are greater than $2000
• Thus, we can directly consider Case-2, where the purchase value is greater than $2000
• Now, let us assume that the purchase value = $x, such that x > $2000
• So, the total tax paid = 5% of $1000 + 10% of ($x – $2000)
• This value should be less than or equal to 4% of x,

o 5% of $1000 + 10% of ($x – $2000) ≤ 4% of x
o \($50 + \frac{10x}{100} - $200 ≤ \frac{4x}{100}\)
o Implies, \(\frac{6x}{100} ≤ $150\)
o Thus, x ≤ $2500