Madhav purchased an item for ₹42,000 and sold it at a loss of 20%. With that amount, he purchased another item and sold it at a gain of 30%. What is the overall gain (in ₹)?

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Step 1: Madhav purchased an item for ₹42,000.

Step 2: He sold it at a loss of 20%.
Loss = 20% of 42,000 = (20/100) × 42,000 = ₹8,400
So, Selling Price (SP1) = Cost Price (CP1) - Loss = 42,000 - 8,400 = ₹33,600

Step 3: With ₹33,600, he purchased another item (CP2 = ₹33,600).

Step 4: He sold this item at a gain of 30%.
Gain = 30% of 33,600 = (30/100) × 33,600 = ₹10,080
So, Selling Price (SP2) = CP2 + Gain = 33,600 + 10,080 = ₹43,680

Step 5: Overall gain = Final Selling Price - Initial Cost Price = 43,680 - 42,000 = ₹1,680

However, let's double-check:

Alternatively, let's use the net effect formula for successive loss and gain:
Net % effect = x + y + (xy/100), where x = -20 (loss), y = +30 (gain)
Net % = -20 + 30 + ((-20)×30)/100 = 10 - 6 = 4%
So, overall gain = 4% of 42,000 = (4/100) × 42,000 = ₹1,680

But this does not match any correct option as per the calculations above. Let's check the stepwise calculation again:

First transaction:
CP1 = 42,000
Loss = 20% → SP1 = 80% of 42,000 = 0.8 × 42,000 = ₹33,600

Second transaction:
CP2 = 33,600
Gain = 30% → SP2 = 130% of 33,600 = 1.3 × 33,600 = ₹43,680

Overall gain = SP2 - CP1 = 43,680 - 42,000 = ₹1,680

But the correct answer as per the options is 6720, which suggests a miscalculation. Let's check the net effect formula for successive loss and gain:

Net effect = (1 - 0.20) × (1 + 0.30) = 0.8 × 1.3 = 1.04
So, net overall = 4% gain
4% of 42,000 = 1,680

But the options suggest 6720 is correct. Let's check if the question is asking for something else.

Wait, let's check if the gain is on the second transaction only:

First, he sells at 20% loss: 42,000 × 0.8 = 33,600
Second, he buys at 33,600 and sells at 30% gain: 33,600 × 1.3 = 43,680
Total gain = 43,680 - 42,000 = 1,680

So, the correct answer is 1,680, but this is option 3. The correct answer is 1,680.

Final answer: Option 3 (1,680)

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