An item costing ₹1640 is being sold at a 15% loss. If the price is further reduced by 40%, then find the selling price.

Correct option is D

Given:

The cost price (CP) of the item = ₹1640.

The item is sold at a 15% loss initially.

The price is further reduced by 40%.

Formula Used:

$$\text{Selling Price} = \text{Cost Price} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right)$$  

$$\text{Final Selling Price} = \text{Selling Price (after first reduction)} \times \left(1 - \frac{\text{Reduction Percentage}}{100}\right)$$​

Solution:

The loss is 15%, so the selling price after the first reduction will be:

Selling Price (SP1) = $$\text{Cost Price} \times \left(1 - \frac{15}{100}\right)$$​​

SP1 = $$1640 \times 0.85 = 1394$$​​

Now, the price is further reduced by 40%. The new selling price will be:

Final Selling Price (SP2) = $$\text{SP1} \times \left(1 - \frac{40}{100}\right)$$​​

SP2 = $$1394 \times 0.60 = 836.4$$​​

The final selling price of the item after both reductions is ₹836.4.

Thus, the correct option is (d) ₹836.4

Alternate Method:

15% = $$-\frac{3}{20}$$, 40% = $$-\frac{2}{5}$$  

CP = 100%,  SP₁= 85%

SP₁ = $$\frac{1680}{100\%} \times 85\%$$

Sp₁ = 1394

SP₂ = 1394 $$\times \frac{3}{5}$$

SP₂ = 836.4

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