A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair. While preparing the bill, the bill clerk interchanged the number of black and brown pair by mistake which increased the bill by 100%. What was the number of pairs of brown socks in the original order?

Correct Option (d)

To determine the number of brown socks, we first define the variables and formulate the costs involved.

• Let the price of one pair of brown socks be x.
• Given that the price of a black pair was thrice that of a brown pair, the price of one pair of black socks is 3x.
• Let the unknown number of pairs of brown socks in the original order be y. The number of black socks in the original order is given as 5 pairs.

The correct bill, based on the original order, would be:

Original Bill = (Number of black pairs × Price of black pair) + (Number of brown pairs × Price of brown pair)

Original Bill = 5 * (3x) + y * x = 15x + xy

Due to the bill clerk's mistake, the number of black and brown pairs was interchanged. Thus, the mistaken bill was calculated for y black pairs and 5 brown pairs:

Mistaken Bill = (Number of black pairs in mistake × Price of black pair) + (Number of brown pairs in mistake × Price of brown pair)

Mistaken Bill = y * (3x) + 5 * x = 3xy + 5x

The problem states that the mistaken bill increased by 100% compared to the original bill. This implies the mistaken bill is twice the original bill:

Mistaken Bill = 2 × Original Bill

3xy + 5x = 2(15x + xy)

Now, we solve this equation for y:

3xy + 5x = 30x + 2xy

Subtract 2xy from both sides of the equation:

xy + 5x = 30x

Subtract 5x from both sides:

xy = 25x

Since x represents a price, it cannot be zero. Therefore, we can divide both sides by x:

y = 25

Thus, the number of pairs of brown socks in the original order was 25.

Incorrect Options:

Options 10, 15, and 20 are incorrect because substituting these values for y into the derived equation 3xy + 5x = 2(15x + xy) would not satisfy the condition that the mistaken bill is precisely 100% higher (i.e., double) than the correct bill. Only y = 25 maintains this proportional relationship between the correct and mistaken bills.