Sameer normally takes 8 hours to drive from Agra to Chandigarh. Today, his car developed some fault at Noida, a city between Agra and Chandigarh. After fixing the fault in 24 minutes, he drove at a speed 25% more than the normal speed. He reached the destination 12 minutes earlier than the normal time. The ratio of the distance between Agra and Noida to that between Noida and Chandigarh is
Answers
Given : Sameer normally takes 8 hours to drive from Agra to Chandigarh. Today, his car developed some fault at Noida, a city between Agra and Chandigarh. After fixing the fault in 24 minutes, he drove at a speed 25% more than the normal speed. He reached the destination 12 minutes earlier than the normal time.
To find : The ratio of the distance between Agra and Noida to that between Noida and Chandigarh is
Solution:
Speed = Distance/Time
Let say Ratio of the distance between Agra and Noida to that between Noida and Chandigarh is k : 1
Distance Agra to Noida = kD km &
Noida to Chandigarh = D km
Total Distance = (k+1)D km
Usual Speed = (k + 1)D/8 km/hr
Time taken till Noida = kD/ ( (k + 1)D/8) = 8k/(k + 1) hr
time in fixing fault = 24 minutes = 24/60 = 2/5 hrs
Speed from Noida to Chandigarh = 25% more than the normal speed.
= ((k + 1)D/8) ( 1 + 25/100)
= ((k + 1)D/8) ( 5/4)
= 5(k + 1)D/32 km/hr
Time taken from Noida to Chandigarh = D/(5(k + 1)D/32) = 32/5(k + 1) hr
Total time taken = 8k/(k + 1) + 2/5 + 32/5(k + 1) hrs
reached the destination 12 minutes = (1/5 hrs)earlier than the normal time.
=> 8k/(k + 1) + 2/5 + 32/5(k + 1) = 8 - 1/5
multiplying both sides by 5(k+1)
=> 40k + 2(k+1) + 32 = 40(k+1) - (k + 1)
=> 40k + 2k + 2 + 32 = 40k + 40 - k - 1
=> 3k = 5
=> k = 5/3
5 : 3 is the Ratio the distance between Agra and Noida to that between Noida and Chandigarh
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