Question

Abdul starts in a car from Ahmedabad towards Bangalore. After some time, he realises that he will cover only 75% of the distance in the scheduled time and he, therefore, doubles his speed immediately and thus manages to reach Bangalore exactly on time. Find the time after which Abdul changed his speed, given that he could have been late by 3 hours if he had not changed his speed:

• A. 3 h
• B. 4 h
• C. 5 h
• D. 6 h

Answer 1

The correct option is D 6 h

Let the original speed be s km/h and scheduled time
= t hours
and total distance = D km
then $s\times t=\frac{3}{4}D...\left(i\right)ands\times (t+3)=D...\left(ii\right)$
From Eq. (i) and (ii), we get
$st=\frac{3}{4}\left[s\right(t+3\left)\right]\Rightarrow t=9h$
and let s = 1 km/h, then D = 12 km
Again, since he doubles his speed after k hours then
$s_1{t}_1+s_2{t}_2=D1\times k+2\times (9-k)=12\Rightarrow 6h$