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.