A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a pair of black socks is double that of a brown pair. While preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50% . The ratio of the number of black and brown pairs of socks in the original order was = ?
Correct Answer: 1 : 4
Black | : | Brown | |
Pairs | 4 | : | x |
Price | 2 | : | 1 |
8 | : | x |
Original bill = 8 + x
Black | : | Brown | |
Pairs | x | : | 4 |
Price | 2 | : | 1 |
2x | : | 4 |
New bill = 2x + 4
According to the question,
$$\eqalign{ & \therefore {\text{3}}\left( {8 + x} \right) = 2\left( {2x + 4} \right) \cr & \Rightarrow 24 + 3x = 4x + 8 \cr & \Rightarrow x = 16 \cr & \therefore {\text{ Brown pairs}} = 16 \cr & \therefore {\text{Black pairs}} = 4 \cr & \therefore {\text{Ratio}} \Rightarrow 1:4 \cr} $$