Shortcut Trick
Use the weighted average logic for parts of the total quantity.
Let the total quantity be 4 units.
1 unit × 12% + 3 units × x% = 4 units × 15%
12 + 3x = 60
3x = 48 ⇒ x = 16%
∴ The correct answer is 16%.
Alternate Method
Given:
Profit on one-fourth (1/4) of wheat = 12%
Overall profit required = 15%
Formula Used:
Overall Profit % = (n1 × p1 + n2 × p2) / (n1 + n2)
Calculations:
Let the total Cost Price (CP) of the wheat be ₹400.
⇒ CP of 1/4 part = 1/4 × 400 = ₹100
⇒ CP of remaining 3/4 part = 3/4 × 400 = ₹300
⇒ Total Profit needed = 15% of 400 = (15/100) × 400 = ₹60
⇒ Profit from 1/4 part = 12% of 100 = (12/100) × 100 = ₹12
⇒ Profit required from remaining part = Total Profit − Profit from 1/4 part
⇒ Required Profit = 60 − 12 = ₹48
⇒ Profit percent on remaining wheat = (Profit / CP of remaining) × 100
⇒ Profit percent = (48 / 300) × 100
⇒ Profit percent = 48 / 3 = 16%
∴ The correct answer is 16%.
Additional Information
Weighted Average Profit
When a commodity is split into parts, the total profit percentage is the sum of (part fraction × its profit percentage) for all parts.
Profit and Loss Basics
Profit % = (Profit/CP) × 100 and Loss % = (Loss/CP) × 100. Always ensure the base is the Cost Price unless specified.
Alligation Method
This can be used to find ratios or mean values. Quantity 1 / Quantity 2 = (Profit 2 − Mean Profit) / (Mean Profit − Profit 1).