Question

A hare pursued by a grey hound is 50 of her own leaps before him. while the hare takes 4 leaps, the grey hound takes 3 leaps. In one leap, the hare goes 1.75 metres and the grey hound 2.75 metres. In how many leaps, will the grey hound overtake the hare?
1. 210 leaps
2. 211 leaps
3. 240 leaps
4. 205 leaps

Answer 1

Correct Answer - Option 2 : 211 leaps

Given:

Grey hound and hare make 3 leaps and 4 leaps respectively. This happens at the same time. 

The greyhound goes 2.75 metres in one leap. 

The hare goes 1.75 metres in 1 leap. 

Calculation:

The hare goes in 4 leaps = 4 × 1.75

⇒ 7 metres

The greyhound goes in 3 leaps = 3 × 2.75

⇒ 8.25 metres

Distance gained by grey hound = (8.25 – 7) = 1.25 metres

Distance covered by hare in 50 leaps = 50 × 1.75

= 87.5  meters

Now, 1.25 metres is gained by greyhound in 3 leaps

so, 87.5 metres is gained in = (3/1.25) × 87.5

⇒ 210 leaps

It will take 210 jumps to catch the hare but to overtake it, it must take one step more

∴ 211 steps will be the correct answer. 

Please see the last line, it is asked how many leaps to overtake the hare, not catching the hare.

It will take 210 jumps to catch the hare but to overtake it, it must take one step more. thus 211 steps will be the correct answer.