Arnav ordered 4 pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue socks. 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)1: 2
(b)1: 4
(c)2: 1
(d)4: 1
Answer
Answer (as printed): B
Explanation
Suppose he ordered $n$ pairs of blue socks. Let the price of each pair of blue socks be ₹ $x$. Then, price of each pair of black socks $=₹ 2 x$. Actual bill $=₹(4 \times 2 x+n x)=₹(8 x+n x)$. Bill made on interchange $=₹(2 n x+4 x)$. $$\begin{aligned} & \therefore \quad 2 n x+4 x=150 \% \text { of }(8 x+n x) \\ & \Rightarrow \quad 2 n x+4 x=\frac{3}{2}(8 x+n x) \\ & \Rightarrow \quad 2(2 n x+4 x)=3(8 x+n x) \\ & \Rightarrow \quad n x=16 x \Rightarrow n=16 \end{aligned}$$ Hence, required ratio $=4: 16=1: 4$.
Explanation as extracted from the printed page; notation may be imperfect.