A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is
- 90
- 100
- 80
- 70
The Correct Option is A
Solution and Explanation
Two cars start from different points and move towards each other. Car 1 travels at 60 km/hr and Car 2 travels at an unknown speed. They meet after \( t \) hours. Given the travel durations for each car's leg of the other's distance, find the speed of Car 2.
Let:
- Speed of Car 2 = \( x \) km/hr
- Time taken by both cars to meet = \( t \) hours
Step 1: Distances traveled
In \( t \) hours:
- Car 1 travels = \( 60 \cdot t \) km
- Car 2 travels = \( x \cdot t \) km
Step 2: Time taken by Car 1 to travel Car 2's distance
Given: Car 1 takes 45 minutes = \( \frac{3}{4} \) hours to cover \( x \cdot t \) km.
\[ \frac{x \cdot t}{60} = \frac{3}{4} \] \[ \Rightarrow t = \frac{180}{4x} \tag{1} \]
Step 3: Time taken by Car 2 to travel Car 1's distance
Given: Car 2 takes 20 minutes = \( \frac{1}{3} \) hours to cover \( 60 \cdot t \) km.
\[ \frac{60 \cdot t}{x} = \frac{1}{3} \] \[ \Rightarrow t = \frac{x}{180} \tag{2} \]
Step 4: Equating both expressions for \( t \)
\[ \frac{180}{4x} = \frac{x}{180} \] \[ \Rightarrow 4x^2 = 180 \cdot 180 = 32400 \] \[ \Rightarrow x^2 = \frac{32400}{4} = 8100 \] \[ \Rightarrow x = \sqrt{8100} = 90 \]
Final Answer: \( \boxed{90 \text{ km/hr}} \)
Correct Option: (A)
Top Questions on Average
- A batch of 36 school children goes for an excursion trip to Nainital. When one 10-year-old child is replaced with another child, the average age of the children in the batch increases by \( 2\frac{1}{2} \) months. What is the age of the new child?
- The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?
What is the sum of ages of Murali and Murugan?
Statements: I. Murali is 5 years older than Murugan.
Statements: II. The average of their ages is 25- If \( a \) and \( b \) are non-negative real numbers such that \( a + 2b = 6 \), then the average of the maximum and minimum possible values of \( (a + b) \) is
- If the average income of seven families is Rs. 4200 and a family with an income of Rs. 1000 joins them, then the average income of all eight families is (in Rs)
Questions Asked in CAT exam
When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?
- CAT - 2024
- Algebra
- A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
- CAT - 2024
- Mensuration
- Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?- CAT - 2024
- Algebra
- Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
- CAT - 2024
- Time and Work