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प्रश्न
If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.
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उत्तर
Let the original speed of the aeroplane be x km/hr.
Time taken to cover a distance of 1200 km = 1200/x hrs
`("Time" = "Distance"/"Speed")`
Let the new speed of the aeroplane be (x – 40) km/hr
Time taken to cover a distance of 1200 km = `1200/(x - 40)` hrs
From the given information, we have
`1200/(x - 40) - 20/60 = 1200/x`
`1200/(x - 40) - 1200/x = 20/60`
`(1200x - 1200x + 48000)/(x(x - 40)) = 1/3`
x(x – 40) = 48000 × 3
x2 – 40x – 144000 = 0
x2 – 400x + 360x – 144000 = 0
x(x – 400) + 360(x – 400) = 0
(x – 400)(x + 360) = 0
x = 400, – 360
But, speed cannot be negative.
So, x = 400.
Thus, the original speed of the aeroplane is 400 km/hr.
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