SSC GD Constable 6 Feb 2025 Shift 1 Paper

Number of yellow bikes $= n_{y}$Number of green bikes $= n_{g}$We know that the total number of bikes is 100 :$n_y + n_g = 100$The average speed of all bikes is given by the weighted average of the speeds of yellow and green bikes:$(n_y \times .$ Average speed of yellow bikes $+n_g \times$ Average speed of green bikes) / Total number of bikes $=$ Average speed of all bikes$\frac{(n_y \times 55 + n_g \times 30)}{100} = 35$Multiply both sides by 100 :$55 \times n_y + 30 \times n_g = 3500$Now we have a system of two equations:$\;n_y + n_g = 100$$\;55 \times n_y + 30 \times n_g = 3500$From equation 1 , we can express $n_{y}$ as:$n_{y} = 100 - n_{g}$Substitute this into equation 2 :$\;55 \times (100 - n_g) + 30 \times n_g = 3500$$\;5500 - 55 \times n_g + 30 \times n_g = 3500$$\;5500 - 25 \times n_g = 3500$Rearrange to solve for $n_{g}$ :$25 \times n_{g} = 5500 - 3500$$\;25 \times n_g = 2000$$\;n_g = \frac{2000}{25}$$\;n_g = 80$