Question

Q.46
Shasha sets off on his bike from Noida to Kanpur, at a
certain speed, intending to reach Kanpur by 5 pm. After
covering a certain distance, he realises that he would be
able to cover only five-eighth of the intended distance by
5 pm. He therefore increases his speed by 75% and
reaches Kanpur at 5 pm. What fraction of the total
distance did he cover at his initial speed?​

Answer 1

Given : Shasha sets off on his bike from Noida to Kanpur, at a  certain speed, intending to reach Kanpur by 5 pm. After  covering a certain distance, he realises that he would be  able to cover only five-eighth of the intended distance by  5 pm. He therefore increases his speed by 75%  and

reaches Kanpur at 5 pm.

To Find : What fraction of the total  distance did he cover at his initial speed ​

Solution:

Let assume Distance of Kanpur  =    8D  km

Speed   required  = 8S  km/hr

Total Time = D/S  hr

Let say Distance covered = x  km

Speed = 5S  km/hr   ( (5/8)8S = 5S )  as he could cover 5/8 of intended distance.

Time take  = x/5S

Distance remaining = 8D - x  km

now Speed  =  5S + (75/100)5S  =  8.75S   km.hr

Time taken = (8D - x)/8.75S

D/S  =  x/5S + (8D - x)/8.75S

=>  8.75D  =1.75x  +  8D - x

=> 0.75D  = 0.75x

=> x /D  = 1

=> x = D

fraction of the total  distance did he cover at his initial speed = x/8D

= D/8D

= 1/8

1/8  fraction of the total  distance  he covered at his initial speed.

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