Question : A person goes from P to Q at a speed of 20 km/hr. Then he goes from Q to R at a speed of $q$ km/hr. Finally, the person goes from R to S at a speed of $r$ km/hr. The distances from P to Q, Q to R and R to S are equal. If the average speed from P to R is $\frac{280}{11}$km/hr, and the average speed from Q to S is $\frac{112}{3}$ km/hr, then what is the value of $r$?
Option 1: 40
Option 2: 37.5
Option 3: 42.5
Option 4: 45
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 40
Solution : The distances from P to Q, Q to R and R to S are equal. Let the distance from P to Q = distance from Q to R = distance from R to S = $y$ Speed of the person from P to Q = 20 km/hr Speed of the person from Q to R = $q$ km/hr Average speed from P to R = $\frac{280}{11}$ km/hr $\frac{y +y}{\frac{y}{20} + \frac{y}{q}} = \frac{280}{11}$ $⇒\frac{2y}{\frac{qy+20y}{20q}} = \frac{280}{11}$ $⇒\frac{2y × 20q}{y(q+20)} = \frac{280}{11}$ $⇒\frac{q}{q+20} = \frac{70}{11}$ $⇒7q + 140 = 11q$ $⇒4q = 140$ $\therefore q = 35$ km/hr Speed of the person from Q to R = $q$ = 35 km/hr Speed of the person from R to S = $r$ km/hr Average speed from P to R = $\frac{112}{3}$ km/hr So, $\frac{y +y}{\frac{y}{35} + \frac{y}{r}} = \frac{112}{3}$ $⇒\frac{2y}{\frac{ry+35y}{35r}} =\frac{112}{3}$ $⇒\frac{2y × 35r}{y(r+35)} = \frac{112}{3}$ $⇒\frac{5r}{r+35} = \frac{8}{3}$ $⇒15r = 8r + 280$ $⇒15r-8r = 280$ $⇒7r = 280$ $⇒r = 40$ km/hr Hence, the correct answer is 40.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : A person walks 10 km at a speed of 2.5 km/hr, then runs 10 km at a speed of 5 km/hr and then goes 30 km by bus at the speed of 30 km/hr. What is the average speed of the man?
Question : A person goes from J to K at a speed of 55 km/hr. He comes back from K to J at a certain speed. If his average speed is $\frac{660}{17}$ km/hr, then what was his speed while moving from K towards J?
Question : A girl goes from M to N at a speed of 25 km/hr and returns to M at a speed of 37.5 km/hr, via the same route. What is the girl's average speed (in km/hr)?
Question : A man goes from A to B at a speed of 200 km/hr and comes back to A at a speed of 300 km/hr. Find his average speed for the entire journey.
Question : A woman drives a car. During her journey, she travels 20 minutes at a speed of 60 km/hr, another 30 minutes at a speed of 40 km/hr and 1 hour at a speed of 50 km/hr. The average speed of the car is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile