Question

[1]
A cyclist takes 2 hours less to cover a distance of 200 km, if he increases his speed by 5 km/hr.
Then his original speed is
a) 26 km/hr
b) 20 km/hr
c) 24 km/hr
d) 25 km/hr
what is the answer​

Answer 1

Answer:

20 kilometer/hour

Step-by-step explanation:

x be time

y be speed

xy = 200(distance)...............1

acc to queston

(x-2) (y+5) =200

xy-2y+5x-10=200

as xy =200  so

5x-2y-10=0

from 1

x = 200/y ........................2

by substituting value of x

Answer 2

The orginial speed of the cyclist = 20 km/hr

Given :

A cyclist takes 2 hours less to cover a distance of 200 km, if he increases his speed by 5 km/hr.

To find :

The orginial speed of the cyclist is

a) 26 km/hr

b) 20 km/hr

c) 24 km/hr

d) 25 km/hr

Solution :

Step 1 of 2 :

Form the equation to calculate orginial speed of the cyclist

Let orginial speed of the cyclist = x km/hr

By the given condition

$\displaystyle \sf \frac{200}{x} - \frac{200}{x + 5} = 2$

Step 2 of 2 :

Calculate orginial speed of the cyclist

$\displaystyle \sf \frac{200}{x} - \frac{200}{x + 5} = 2$

$\displaystyle \sf{ \implies }\frac{200(x + 5) - 200x}{x(x + 5)} = 2$

$\displaystyle \sf{ \implies }\frac{200x +1000 - 200x}{ {x}^{2} + 5x } = 2$

$\displaystyle \sf{ \implies }\frac{1000 }{ {x}^{2} + 5x } = 2$

$\displaystyle \sf{ \implies } {x}^{2} + 5x = 500$

$\displaystyle \sf{ \implies } {x}^{2} + 5x - 500 = 0$

$\displaystyle \sf{ \implies } {x}^{2} + (25 - 20)x - 500 = 0$

$\displaystyle \sf{ \implies } {x}^{2} + 25x - 20x - 500 = 0$

$\displaystyle \sf{ \implies }x(x + 25) - 20(x + 25) = 0$

$\displaystyle \sf{ \implies }(x + 25) (x - 20) = 0$

x + 25 = 0 gives x = - 25

x - 20 = 0 gives x = 20

Since orginial speed of the cyclist can not be negative

∴ x ≠ - 25

∴ x = 20

So orginial speed of the cyclist = 20 km/hr

Hence the correct option is b) 20 km/hr

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