Question 61

Due to 20% reduction in the price of wheat per kg, Ram is able to by 5 kg more for ₹800. What is the original quantity (in kg) of wheat?

Let the original price of wheat be $$x$$ rupees per kg and the original quantity that Ram could buy for ₹800 be $$q$$ kg.

Money spent = price × quantity, therefore
$$800 = q \times x \quad -(1)$$

The price is reduced by 20%, so the new price per kg is
$$\text{new price} = x - 0.20x = 0.8x$$

With the same ₹800, the new quantity bought is
$$\text{new quantity} = \frac{800}{0.8x} = \frac{1000}{x} \text{ kg}$$

According to the question, this new quantity is 5 kg more than the original quantity:
$$\frac{1000}{x} - q = 5 \quad -(2)$$

Substitute $$q = \frac{800}{x}$$ from $$(1)$$ into $$(2)$$:

$$\frac{1000}{x} - \frac{800}{x} = 5$$
$$\frac{200}{x} = 5$$
$$x = \frac{200}{5} = 40 \text{ rupees per kg}$$

Now find the original quantity using $$(1)$$:
$$q = \frac{800}{x} = \frac{800}{40} = 20 \text{ kg}$$

Hence, the original quantity of wheat Ram could buy was 20 kg.

Option B which is: 20

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