Mathematics 2017 Jamb Examination

Let the first speed be \( v \) and the first distance be \( d_1 = 50 \). The first time is \( t_1 = \frac{50}{v} \). For the second trip, the distance is \( d_2 = 300 \) and the speed is \( 3v \). The second time is: \[ t_2 = \frac{300}{3v} = \frac{100}{v} \] Comparing \( t_2 \) to \( t_1 \): \[ \frac{t_2}{t_1} = \frac{100/v}{50/v} = 2 \] So, the new time is twice as much.

The sum of angles at a point is \( 360^\circ \). \[ 2x + 3x + 4x = 360^\circ \] \[ 9x = 360^\circ \] \[ x = \frac{360^\circ}{9} = 40^\circ \]

\[ \begin{array}{r|l}
2x - 1 & 4x^3 + 0x^2 - 3x + 1 \\
\hline
& 2x^2 + x - 1 \\[4pt]
& 4x^3 - 2x^2 \\
& \underline{\phantom{4x^3}2x^2 - 3x + 1} \\[4pt]
& 2x^2 - x \\
& \underline{\phantom{4x^3 + 0x^2}-2x + 1} \\[4pt]
& -2x + 1 \\
& \underline{\phantom{4x^3 + 0x^2 + 0x}0}
\end{array}\]

Total Cost Price (CP) = Purchase Price + Refurbishing Cost \[ CP = 250,000 + 70,000 = 320,000 \] Selling Price (SP) = 400,000 Gain = \( SP - CP = 400,000 - 320,000 = 80,000 \) \[ \text{Percentage Gain} = \frac{\text{Gain}}{CP} \times 100 = \frac{80,000}{320,000} \times 100 \] \[ = \frac{1}{4} \times 100 = 25\% \]

The word EXCELLENCE has 10 letters. Count the repetitions: - E appears 4 times - C appears 2 times - L appears 2 times - X, N each appear 1 time. The number of arrangements is given by: \[ \frac{10!}{4!2!2!} \]