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प्रश्न
An aeroplane takes 1 hour less for a journey of 1200km, if its speed is increased by 100km/ hrfrom its usual speed. Find the usual speed.
उत्तर
Let the Usual Speed of the aircraft be S, and time taken be t. Distance = 1200km
Time = Distance/ Speed.
Time taken is reduced by 1 hr when speed increases by 100 km/ hr
`1200/"S" = 1200/("S" + 100) + 1`
`=> (1200 + "S" + 100)/("S" + 100) = 1200/"S"`
⇒ 1300S + S2 = 1200 S + 120000
⇒ S2 + 100 S - 120000 = 0
⇒ S2 + 400 S - 300 S - 120000 = 0
⇒ S (S + 400) - 300 (S + 400) = 0
⇒ (S + 400) (S - 300) = 0
⇒ S= -400 ,300
Speed cannot be negative .
Hence, S=300 km/ kr
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