मराठी

A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed. - Mathematics

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प्रश्न

A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.

बेरीज
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उत्तर

Time taken by a man = `100/x` hrs.

Now, New speed of man = (x + 5) km/hr

∴ Time taken by a man = `100/((x + 5))` hrs.

According to question,

`100/x - 100/(x + 5)` = 1 hour

`100[1/x - 1/(x + 5)]` = 1

`100[(x + 5 - x)/(x(x + 5))]` = 1

500 = x(x + 5)

x2 + 5x – 500 = 0

x2 + 25x – 20x – 500 = 0

x(x + 25) – 20(x + 25) = 0

(x + 25)(x – 20) = 0

x = 20 or x = – 25   ...(Speed cannot be negative)

Hence x = 20 km/hour

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पाठ 5: Quadratic equations - Exercise 5E [पृष्ठ ९२]

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नूतन Mathematics [English] Class 10 ICSE
पाठ 5 Quadratic equations
Exercise 5E | Q 26. | पृष्ठ ९२

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