Question

Rohit and rahul start from the same point and move away from each other at right angle. after 4 hours they are 80 km apart. if the speed of rohit is 4 kmph more than rahul. what is the speed of rohit?
a. 16 kmph
b. 20 kmph
c. 12 kmph
d. none

Answer 1

speed of Rohit 16 kmph

Answer 2

Answer:

Speed of Rohit is found to be 16 kmph . The correct option is (a).

To find:

Speed of Rohit

Solution:

Given : Rohit and Rahul start at the same point and they each other move in a right angle. They are separated by 80 km after 4 hours.  

Rahul’s speed is 4 kmph less than Rohit’s.  

Let speed of Rahul be x.

Then, Distance covered by Rahul = Speed × Time

$\begin{aligned} & = 4 \times x \\\\ = & 4 x k m p h \end{aligned}$

& speed of Rohit is 4kmph more than Rahul. Hence,

Rohit covered 4(x + 4)kmph

Now, by Pythagoras theorem,

$a^2+b^2+c^2$ whereas a = 4x, b = 4 (x + 4) and c = 80kmph

$\begin{aligned} ( 4 x ) ^ { 2 } + [ 4 ( x + 4 ) ] ^ { 2 } & = ( 80 ) ^ { 2 } \\\\ 16 x ^ { 2 } + 16 \left( x ^ { 2 } + 8 x + 16 \right) & = 80 \times 80 \\\\ 16 \left( x ^ { 2 } + x ^ { 2 } + 8 x + 16 \right) & = 16 ( 5 ) \times 80 \\\\ \left( 2 x ^ { 2 } + 8 x + 16 \right) & = 400 \end{aligned}$

$\begin{array} { c } { \left( x ^ { 2 } + 4 x + 8 \right) = 200 } \\\\ { x ^ { 2 } + 4 x + 8 - 200 = 0 } \\\\ { x ^ { 2 } + 4 x - 192 = 0 } \\\\ { x ^ { 2 } + 16 x - 12 x - 192 = 0 } \\\\ { x ( x + 16 ) - 12 ( x + 16 ) = 0 } \\\\ { ( x - 12 ) ( x + 16 ) = 0 } \end{array}$

Hence, x = -16 or x = 12.

Now speed cannot be minus, thus

x = 12 kmph i.e. Speed of Rahul

Speed of Rohit = x + 4 = 12 + 4 = 16 kmph