# A dishonest trader makes a profit of 20% normally. Due to an error, the weight machine measures 900 instead of 1kg. If he charges 25% less what he nor

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A dishonest trader makes a profit of 20% normally. Due to an error, the weight machine measures 900 instead of 1kg. If he charges 25% less what he normally charges which of the following is correct?

I. He makes a profit of 5%

II. incurs a loss of 5%

III. There is no profit no loss

IV. The ratio of CP of 900 gm to that of final SP is 1 : 1

1. Only I
2. Only II
3. Only III
4. III and IV

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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.