Let's break down the problem step by step.

Step 1: Marked Price

The trader marked up his goods by 70%. So, if the cost price (C.P.) of the goods is $100$ units, then the marked price (M.P.) is: $M.P. = C.P. \times (1 + 0.70) = 100 \times 1.70 = 170$

Step 2: Discount

The trader then gives a discount of 20% on the marked price. So, the selling price (S.P.) becomes: $S.P. = M.P. \times (1 - 0.20) = 170 \times 0.80 = 136$

Step 3: Faulty Balance

The trader uses a faulty balance that weighs 15% less than the actual weight. This means he is selling only 85% of the goods that he claims to sell. Therefore, the selling price he receives is for only 85% of the goods, while the cost price is for 100%.

So, the effective cost price (E.C.P.) is reduced because he's effectively selling 85% of the goods. The new effective cost price is: $E.C.P. = C.P. \times 0.85 = 100 \times 0.85 = 85$

Step 4: Profit Calculation

Now, the trader's profit is the difference between the selling price and the effective cost price. The percentage profit is: $\text{Profit} = \frac{S.P. - E.C.P.}{E.C.P.} \times 100 = \frac{136 - 85}{85} \times 100 = \frac{51}{85} \times 100 \approx 60\%$

Conclusion:

The correct answer is 4) 60%.

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Do you want further clarification on any part of this solution?

Here are 5 related questions for further practice:

1. If a trader marks up goods by 50% and gives a 10% discount, what is the profit if there is no faulty balance?
2. What would the profit percentage be if the faulty balance weighed 10% less instead of 15%?
3. If the trader gave a discount of 30% instead of 20%, what would the new profit percentage be?
4. How would the calculation change if the trader's faulty balance weighed 20% less?
5. If the trader had marked up his goods by 100%, what would his profit percentage be with the same discount and faulty balance?

Tip: Always break down the problem into steps like cost price, selling price, and adjustments for faulty equipment to simplify complex calculations.