Question

A cat seeing a mouse in front of it , starts to catch it .In the same interval of time the cat jumps 8 times and the mouse jumps 6 times. But the distance covered by the cat in 7 jumps is equal to the distance covered by the mouse in 5 jumps . find the ratio of the speeds if the cat and mouse​

Answer 1

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

Answer 2

Answer:

20:21 is answer

their ratio is 20:21