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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 2 · Set 2 · Q34
(a) In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual…
In a flight of $\displaystyle 600$ km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by $\displaystyle 200$ km/h from its usual speed and time of flight increased by $\displaystyle 30$ minutes. Find the scheduled duration of the flight.
Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for $\displaystyle 4$ hours and the pipe of the smaller diameter for $\displaystyle 9$ hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes $\displaystyle 10$ hours more than the pipe of larger diameter to fill the pool.
Marking-scheme solution
Let the average speed of the aircraft be x km/h
Time taken by aircraft \(\displaystyle =\frac{600}{\mathrm{x}}\)
Time taken by aircraft when flight is delayed by \(\displaystyle 30 \mathrm{~min}=\frac{600}{\mathrm{x}-200}\)
\(\displaystyle \Rightarrow \mathrm{x}^{2}-200 \mathrm{x}-240000=0\)
\(\displaystyle \Rightarrow \quad(\mathrm{x}-600)(\mathrm{x}+400)=0\)
\(\displaystyle \Rightarrow \quad \mathrm{x}=600, \mathrm{x}=-400\)
\(\displaystyle \mathrm{x}=-400\) (rejected)
\(\displaystyle \therefore \mathrm{x}=600\)
∴ Scheduled duration of the flight \(\displaystyle =\frac{600}{600}=1\) hour
Let time taken to fill the pool by larger diameter pipe alone be x hours
Time taken to fill the pool by smaller diameter pipe alone \(\displaystyle =(\mathrm{x}+10)\) hours
\(\displaystyle \frac{4}{x}+\frac{9}{x+10}=\frac{1}{2}\)
\(\displaystyle \Rightarrow \quad \mathrm{x}^{2}-16 \mathrm{x}-80=0\)
\(\displaystyle \Rightarrow \quad(\mathrm{x}+4)(\mathrm{x}-20)=0\)
\(\displaystyle \Rightarrow \quad \mathrm{x}=-4, \mathrm{x}=20\)
\(\displaystyle \mathrm{x}=-4(\) rejected \(\displaystyle )\)
\(\displaystyle \therefore \mathrm{x}=20\)
Time taken to fill the pool by larger diameter pipe alone = $\displaystyle 20$ hours
Time taken to fill the pool by smaller diameter pipe alone = $\displaystyle 30$ hours
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.