Correct Answer - Option 4 :
III and IV
Given:
The trader makes a profit of 20% normally
Weight machine measures 900 instead of 1kg
He charges 25% less what he normally charges
Formula Used:
Profit = SP – CP
Profit% = (Profit /CP) × 100
SP = {(100 + P%)/100} × CP
Where CP is cost price and SP is selling price
Calculation:
Let the cost price of 1 kg is CP
Original selling price = {(100 + P%)/100} × CP
⇒ (120/100) × CP
Cost price of 1000 gm = CP
⇒ Cost price of 900 gm = (9/10)CP
He charges 25% less what he normally charges
⇒ SP = 75% of (120/100) × CP
⇒ SP = (75/100) × (120/100) × CP
⇒ SP = [(3 × 6)/(4 × 5)] × CP
⇒ SP = 0.9 CP
⇒ SP = 9/10CP
⇒ Cost price of 900 gm = 9/10CP
There is no profit no loss in this transaction
CP of 900 gm ∶ SP = 1 ∶ 1
∴ III and IV are correct.
Short Trick:
Let the CP is 100 and solve as above.