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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 3 · Set 1 · Q32
(a) In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by doing so, the time of…
(a)
In a flight of $\displaystyle 2800$ km, an aircraft was slowed down due to bad weather. Its average speed is reduced by $\displaystyle 100$ km/h and by doing so, the time of flight is increased by $\displaystyle 30$ minutes. Find the original duration of the flight.
OR
(b)
The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is $\displaystyle 2 \frac{16}{21}$, find the fraction.
Marking-scheme solution
Let original speed of aircraft be x km/hr.
A.T.Q.
\[\begin{aligned}
& \frac{2800}{x-100}-\frac{2800}{x}=\frac{1}{2} \\
& \Rightarrow x^{2}-100 x-560000=0 \\
& \Rightarrow(x-800)(x+700)=0 \\
& x \neq-700 \text { So, } x=800
\end{aligned}
\]
Original Duration \(\displaystyle =\frac{2800}{800}=\frac{7}{2} \mathrm{hrs}\) or $\displaystyle 3$ hrs $\displaystyle 30$ min.
Let numerator be x , then denominator be \(\displaystyle (2 \mathrm{x}+1)\)
\[\text { Fraction }=\frac{x}{2 x+1}
\]
A.T.Q.
\[\begin{aligned}
& \frac{x}{2 x+1}+\frac{2 x+1}{x}=\frac{58}{21} \\
\Rightarrow & 11 x^{2}-26 x-21=0 \\
\Rightarrow & (x-3)(11 x+7)=0 \\
& x \neq-\frac{7}{11} \text { So, } x=3 \\
\therefore & \text { Fraction }=\frac{3}{7}
\end{aligned}
\]
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