Question

John ordered $4$ pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice of the blue. When the order was filled, it was found that the number of pairs of the two colours had been interchanged. This increased the bill by $50$%. The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was

• A. $4:1$
• B. $2:1$
• C. $1:4$
• D. $1:2$

Answer 1

The correct option is C $1:4$

Given number of pair of black socks $=4$

Let the number of pair of blue socks be $x$

Let the price of the blue socks per pair be $Rs.y$

$\therefore$ The price of the black socks per pair be $Rs.2y$

$\Rightarrow$ The original bill $=(4\times 2y+x\times y)=8y+xy$

$\Rightarrow$ The new bill after interchanged $=(4\times y+x\times 2y)=4y+2xy$

The new bill is $50\%$ more than the original bill.

$\therefore$ $(8y+xy)+(8y+xy)\times \frac{50}{100}=4y+2xy$

$\Rightarrow$ $(8y+xy)+\frac{(8y+xy)}{2}=4y+2xy$

$\Rightarrow$ $\frac{3}{2}\times (8y+xy)=4y+2xy$

$\Rightarrow$ $\frac{3}{2}(8+x)=4+2x$ [ Dividing both sides by $y$ ]

$\Rightarrow$ $3(8+x)=2(4+2x)$

$\Rightarrow$ $24+3x=8+4x$

$\Rightarrow$ $4x-3x=24-8$

$\Rightarrow$ $x=16$

$\therefore$ The number of blue socks in the original bill are $16$

$\Rightarrow$ The required ratio $=\frac{4}{16}=\frac{1}{4}$