Question

A shopkeeper marked a watch 25% above its cost price, sold it with a 15% discount, and received \$850. Find the cost price.

Hint:

For markup-discount problems, always multiply the markup factor and the discount factor to get the overall selling price factor, then equate to the given SP to find the cost price.

Answer 1

Solution:
Step 1 (Let the cost price be \(C\)).
Marked Price (MP) is 25% above cost price: \[ MP = C + 0.25C = 1.25C \] Step 2 (Apply the 15% discount).
Selling Price (SP) after discount: \[ SP = MP - 0.15(MP) = 0.85 \times MP \] Substitute \(MP = 1.25C\): \[ SP = 0.85 \times 1.25C = 1.0625C \] Step 3 (Relate SP to given value).
Given \(SP = 850\): \[ 1.0625C = 850 \] \[ C = \frac{850}{1.0625} = 1000 \] Step 4 (Verification).
Cost price = \$1000 MP = \(1000 \times 1.25 = 1250\) Discounted price = \(1250 \times 0.85 = 1062.5\) — Wait, this is incorrect based on given \$850. Correction:} The above suggests mismatch; let’s re-check: If MP = \(1.25C\) and discount 15% SP = \(0.85 \times 1.25C = 1.0625C\). Given SP = 850, indeed: \[ C = \frac{850}{1.0625} = 800 \] Now correct values: Cost Price = \$800, MP = \(1.25 \times 800 = 1000\), SP = \(1000 \times 0.85 = 850\) ✔️ \[ {\$800} \]