Question

A trader marked up shirts by 40%, offered a 20% discount during a sale, and sold each for 234. Find the number of shirts he purchased. 
 

Hint:

In multi-step markup-discount problems, calculate the effective multiplier from cost to selling price, then use given values to deduce missing quantities.

Answer 1

Solution:
Step 1 (Let the cost price per shirt be \(C\)).
Marked Price: \[ MP = C + 0.40C = 1.4C \] Step 2 (Apply the 20% discount).
Selling Price per shirt: \[ SP = 0.80 \times MP = 0.80 \times 1.4C = 1.12C \] Step 3 (Relate SP to given value).
Given \(SP = 234\): \[ 1.12C = 234 C = \frac{234}{1.12} = 208.93 \ (\approx 209) \] Step 4 (Find number of shirts).
If total cost or revenue were given, number of shirts \(n\) would be computed as: \[ n = \frac{\text{Total Revenue}}{\text{SP per shirt}} \] Since the total amount is not specified in the visible data, we can’t directly determine \(n\) without that figure. Assuming total revenue = \$5850 (for example), \[ n = \frac{5850}{234} = 25 \] \[ {\text{25 shirts (if total revenue = \$5850)}} \]