1.

A cat sees a mouse in front of himRan to catch. At the same time the cat is 4 times and the rat is 6 timesJump the bar. But the cat jumped 7 times that distanceThe rat crossed that distance by jumping 5 times. Ratio of speed of cat and rat​

Answer»

Given :

The no of jumps by CAT is 8 and by MOUSE is 6 in same interval of time .

Distance covered by cat in 7 jumps is equal to that by mouse in 5 jumps .

To Find :

Ratio of speeds of cat and mouse = ?

Solution :

Let the given same interval of time be t .

So, time TAKEN by cat for 1 jump = \frac{8}{t}

And , time taken by mouse for 1 jump = \frac{6}{t}

Let the equal distance covered be = x

So, the time taken by cat to cover x in 7 jumps = \frac{7 \times 8}{t}

=\frac{56}{t}

And the time taken by mouse to cover x in 5 jumps = \frac{5 \times 6}{t}

= \frac{30}{t}

So , the speed of cat = \frac{x}{\frac{56}{t}} = \frac{xt}{56}

And speed of mouse = \frac{x}{\frac{30}{t}} = \frac{xt}{30}

So, the ratio of speeds :

=\frac{(\frac{xt}{56})}{(\frac{xt}{30})}

=\frac{30}{56}

=\frac{15}{28}

Hence , ratio of their speeds is 15 : 28


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