Question

Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes (4/5)th of the original speed. So, he travels the rest of the distance at a constant speed (4/5)th of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?

Answer 1

Explanation:

Given Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes (4/5)th of the original speed. So, he travels the rest of the distance at a constant speed (4/5)th of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?

• Let the distance from Delhi to Gurgaon be m kms.
• So after 30 kms we have m – 30 kms
• So after 48 kms we have m – 48 kms
• Assume initial or original speed be p km/hr
• So time taken will be 18/p x 4/5 (48 – 30 = 18)
• So time taken will be more to the extent of 9 min.
• So we have 18 / p x 4/5 – 18 / p = 9/60 (45-36 = 9)
•                So 5/4 x 18/p – 18/p = 9/60
•                     18 / p x ¼ = 9/60
•                   Or p = 30 km/hr
• So revised speed will be 4/5 (original speed)
•                                     4/5 x 30
•                                        24 km / hr
• So m – 30 travel at 24 km/hr and m – 30 travel at 30 km/hr and so difference is 45 minutes.
• So assume some constant k we have k/30 and k/ 24 and the difference between them will be k/24 – k/30 = ¾
• Or k/120 = ¾  
• Or k = 90 kms
• Now total distance = 90 + 30 = 120 kms
• OR
• We can do as m – 30 / m – 48 = ¾ / 3/5 [ ¾ because 45/60 and 3/5 because 36/60]
• So m – 30 / m – 48 = 5/4
• So 4(m – 30) = 5(m – 48)
• So 4m – 120 = 5m – 240
• Or m = 240 – 120
• Or m = 120 km
• Therefore distance between Delhi and Gurgaon is 120 km  

Reference link will be

https://brainly.in/question/46520

Answer 2

Answer:

120km will be the correct answer hope it helps you