Question

if a man travels at 30km/hr, he reaches his destination late by 10 min. and if he travels at 42km/hr then he reaches 10 min. earlier. How far did he travel ?.

Answer 1

Let Actual Time=x×60 minutes (1 hour=60 min)

Now,1st
Speed=30 km/h=5/10 km/min. (Divide speed by 60)

It take 10 min more.
Now Time taken
Time=(x×60)+10
Distance=5/10(60x+10) km
=300x/10+50/10 km

Now 2nd
Speed=42 km/h=7/10 km/min (Divide speed by 60)

It take 10 min less
Now Time taken
Time=(x×60)-10
Distance=7/10(60x-10)
=420x/10-70/10

Now Both Distance is same
300x/10+50/10=420x/10-70/10
=300x/10-420x/10=-70/10-50/10
=-120x/10=-120/10
=120x/10=120/10. (- -=+)
=x=120/10×10/120
x=1

Now Pick any Distance
300x/10+50/10
300×1/10+50/10
=300/10+50/10
=350/10
=35 km

Distance=35 km

He travel=35 km