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Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.
- a)858
- b)600
- c)400
- d)200
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Raja and Joseph start from their school to walk towards their hostel....
Let R and J be the length of each step of Raja and Joseph respectively.
View all questions of this test
We can write the following equations based on the given information:
3R = 4J
and 800R – 800 J = 300 m
Solving, we get R = 1.5 m = 150 cm and J = 112.5 cm
Revised value for length of each step of Raja R1 = 
and for Joseph, J1 = 112.5 + (20% of 112.5) = 135 cm
Once again, difference in the length of a step of Raja and Joseph = 35 cm with Joseph’s step being longer. In order to catch up with Raja who is ahead of him by 300 m, the number of steps required = 300/ 0.35 = 857.14 = 858
since step can’t be written in fraction so we can write it & the result is found is more than 857 so the answer would be 858.
Most Upvoted Answer
Raja and Joseph start from their school to walk towards their hostel....
To solve this problem, let's break it down step by step.
Given information:
- Raja covers the same distance in 3 steps as Joseph does in 4 steps.
- The time taken by both of them to cover a step is identical.
- At a particular instance when both had covered 800 steps each, the distance between them was 300 m.
Step 1: Calculate the distance covered by Raja and Joseph in a single step
Let's assume the distance covered by Raja in a single step is "x" meters.
Since Joseph covers the same distance in 4 steps as Raja does in 3 steps, the distance covered by Joseph in a single step is (3/4)x meters.
Step 2: Calculate the initial distance between Raja and Joseph
At the particular instance when both had covered 800 steps each, the distance covered by Raja is 800x meters and the distance covered by Joseph is 800(3/4)x = 600x meters.
Given that the distance between them was 300 meters, we can write the equation:
800x - 600x = 300
200x = 300
x = 300/200
x = 1.5 meters
Step 3: Calculate the number of steps required for both to meet
Raja cuts down the length of his step by 1/3rd, so the new distance covered by Raja in a single step is (1 - 1/3)x = (2/3)x meters.
Joseph increases the length of his step by 20%, so the new distance covered by Joseph in a single step is (1 + 20/100)(3/4)x = (9/5)x meters.
Let's assume the number of additional steps required for both to meet is "n".
The distance covered by Raja after n steps = 800(2/3)x + n(2/3)x
The distance covered by Joseph after n steps = 800(9/5)x + n(9/5)x
Since they meet at the same spot, we can write the equation:
800(2/3)x + n(2/3)x = 800(9/5)x + n(9/5)x
Simplifying the equation:
(800(2/3) - 800(9/5))x = (9/5 - 2/3)nx
(16/15 - 72/15)x = (27/15 - 10/15)nx
-56/15x = 17/15nx
-56/17 = nx
Therefore, the number of additional steps required for both to meet is 56/17.
Adding the initial 800 steps, the total number of steps required = 800 + 56/17 = 858.
Therefore, both Raja and Joseph will be at the same spot at the same time after 858 more steps.
Given information:
- Raja covers the same distance in 3 steps as Joseph does in 4 steps.
- The time taken by both of them to cover a step is identical.
- At a particular instance when both had covered 800 steps each, the distance between them was 300 m.
Step 1: Calculate the distance covered by Raja and Joseph in a single step
Let's assume the distance covered by Raja in a single step is "x" meters.
Since Joseph covers the same distance in 4 steps as Raja does in 3 steps, the distance covered by Joseph in a single step is (3/4)x meters.
Step 2: Calculate the initial distance between Raja and Joseph
At the particular instance when both had covered 800 steps each, the distance covered by Raja is 800x meters and the distance covered by Joseph is 800(3/4)x = 600x meters.
Given that the distance between them was 300 meters, we can write the equation:
800x - 600x = 300
200x = 300
x = 300/200
x = 1.5 meters
Step 3: Calculate the number of steps required for both to meet
Raja cuts down the length of his step by 1/3rd, so the new distance covered by Raja in a single step is (1 - 1/3)x = (2/3)x meters.
Joseph increases the length of his step by 20%, so the new distance covered by Joseph in a single step is (1 + 20/100)(3/4)x = (9/5)x meters.
Let's assume the number of additional steps required for both to meet is "n".
The distance covered by Raja after n steps = 800(2/3)x + n(2/3)x
The distance covered by Joseph after n steps = 800(9/5)x + n(9/5)x
Since they meet at the same spot, we can write the equation:
800(2/3)x + n(2/3)x = 800(9/5)x + n(9/5)x
Simplifying the equation:
(800(2/3) - 800(9/5))x = (9/5 - 2/3)nx
(16/15 - 72/15)x = (27/15 - 10/15)nx
-56/15x = 17/15nx
-56/17 = nx
Therefore, the number of additional steps required for both to meet is 56/17.
Adding the initial 800 steps, the total number of steps required = 800 + 56/17 = 858.
Therefore, both Raja and Joseph will be at the same spot at the same time after 858 more steps.
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Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer?
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Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer?.
Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Raja and Joseph start from their school to walk towards their hostel. The distance covered by Raja in 3 steps is identical to the distance covered by Joseph in 4 steps while the time taken by both of them to cover a step is identical. At a particular instance of time when both of them had covered 800 steps each, the distance between them was 300 m. Now, Raja cuts down the length of his step by 1/3rd and Joseph increase the length of his step by 20% with time taken to cover a step by both remaining identical. Both will be at the same spot at the same time in ______ more steps.a)858b)600c)400d)200Correct answer is option 'A'. Can you explain this answer?.
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