Question:
A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option.
A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option.
Updated On: Dec 5, 2024
- I alone is sufficient to solve the problem
- II alone is sufficient to solve the problem
- Either of I or II, by itself, is sufficient to solve the problem.
- I and II both are required to solve the problem.
- The problem cannot be solved even with both I and II.
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Analyze the given data and statements. From statement I: - The ground dimensions are 80m × 50m. - This determines the positions of Raju and Ratan at the mid-points of the shorter sides (at (25, 0) and (25, 80), respectively).
From statement II: - The area of the triangle formed by Raju, Rivu, and Ratan is 1,000 square metres. - Using the formula for the area of a triangle:
Area \(= \frac{1}{2} \times \text{base} \times \text{height},\)
where the base is the distance between Raju and Ratan (80m), we can find Rivu's coordinates.
Step 2: Calculate the time taken. The speed of the ball is constant at 10m/s. Using the coordinates of Rivu, the distances between Raju, Rivu, and Ratan can be determined, and hence the total time can be calculated:
Time \(= \frac{\text{Total Distance}}{\text{Speed}} + \text{Holding Time.}\)
Both statements I and II are necessary to calculate the total distance and time.
Answer: I and II both are required to solve the problem.
Was this answer helpful?
0
0
Top Questions on Geometry
- Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other (see the image below).
If AB = 18 cm and BC = 24 cm, then find the value of r.
- A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal sides meet, to the base, is 200 feet.
To counter the adverse effect of climate change, the farmer wants to dig a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle from inside.
If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land from his neighbour for the pond? (Choose the closest option.) - A rectangle \(ABCD\) has sides \(AB = 45 \, \text{cm}\) and \(BC = 26 \, \text{cm}\). Point \(E\) is the midpoint of side \(CD\). Find the radius of the incircle of the triangle \(\triangle AED\).
- PQR is a triangle. The bisectors of the internal angle ∠Q and external angle ∠R intersect at M. If ∠QMR = 40°, then ∠P is:
- In a triangle PQR, if ∠P + ∠R = 150° and ∠P + 3∠Q = 170°, then ∠P is:
View More Questions
Questions Asked in XAT exam
- Consider a 4-digit number of the form abbb, i.e., the first digit is a (a > 0) and the last three digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4- digit number is divisible by a?- XAT - 2024
- Number Systems
- FS food stall sells only chicken biryani. If FS fixes a selling price of Rs. 160 per plate, 300 plates of biriyani are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then what is the maximum profit that FS can achieve in a day?- XAT - 2024
- Profit and Loss
- Read the following statement carefully.
___________like a fake can be a sign of___________, and clinging too tightly to what feels like one’s authentic self can ________that growth.
Fill in the blanks meaningfully, in the above statement, from the following options- XAT - 2024
- Fill in the Blanks
- Tech predictions often fail not because of wrong models or a lack of imagination, but due to lack of humility in admitting our uncertainty about the future.( Maximum 250 words )
- XAT - 2024
- Analytical Decision Making
- "Things which matter most must never be at the mercy of things which matter least."( Maximum 250 words)
- XAT - 2024
- Time Management
View More Questions