CAT Exam > CAT Questions > A sum is to be distributed among certain numb...
Start Learning for Free
A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.?
Most Upvoted Answer
A sum is to be distributed among certain number of persons. Second per...
Problem:
A sum is to be distributed among a certain number of persons. The second person gets one rupee more than the first, the third person gets two rupees more than the second, the fourth person gets three rupees more than the third, and so on. If the first person gets one rupee and the last person gets 67 rupees, find the number of persons.
Solution:
Let's assume that there are n persons in total.
Step 1: Setting up the problem
Let's denote the amount of money received by the first person as x.
According to the given information, the second person receives one rupee more than the first person, so the second person receives x + 1.
Similarly, the third person receives two rupees more than the second person, so the third person receives x + 1 + 2 = x + 3.
Continuing this pattern, the last person receives 67 rupees, so the last person receives x + (n-1).
We can now create an equation based on the given information.
Step 2: Formulating the equation
The sum of the amounts received by all the persons should be equal to the total amount of money distributed. In this case, the total amount is the sum of the money received by each person, which can be represented as:
x + (x + 1) + (x + 3) + ... + (x + (n-1)) = total amount
Given that the first person receives one rupee, we have x = 1. Substituting this value into the equation, we get:
1 + (1 + 1) + (1 + 3) + ... + (1 + (n-1)) = total amount
Simplifying further, we have:
1 + 2 + 3 + ... + (n-1) = total amount - n + 1
Step 3: Solving the equation
The sum of consecutive numbers from 1 to (n-1) can be calculated using the formula:
Sum = (n-1)(n)/2
Substituting this into the equation, we have:
(n-1)(n)/2 = total amount - n + 1
Since the total amount is 67 rupees, we can substitute it into the equation:
(n-1)(n)/2 = 67 - n + 1
Simplifying further, we get:
n^2 - 3n - 132 = 0
Step 4: Solving the quadratic equation
We can solve the quadratic equation by factoring or using the quadratic formula. Factoring is not possible in this case, so we will use the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
For the given equation, a = 1, b = -3, and c = -132. Substituting these values into the quadratic formula, we get:
n = (-(-3) ± √
A sum is to be distributed among a certain number of persons. The second person gets one rupee more than the first, the third person gets two rupees more than the second, the fourth person gets three rupees more than the third, and so on. If the first person gets one rupee and the last person gets 67 rupees, find the number of persons.
Solution:
Let's assume that there are n persons in total.
Step 1: Setting up the problem
Let's denote the amount of money received by the first person as x.
According to the given information, the second person receives one rupee more than the first person, so the second person receives x + 1.
Similarly, the third person receives two rupees more than the second person, so the third person receives x + 1 + 2 = x + 3.
Continuing this pattern, the last person receives 67 rupees, so the last person receives x + (n-1).
We can now create an equation based on the given information.
Step 2: Formulating the equation
The sum of the amounts received by all the persons should be equal to the total amount of money distributed. In this case, the total amount is the sum of the money received by each person, which can be represented as:
x + (x + 1) + (x + 3) + ... + (x + (n-1)) = total amount
Given that the first person receives one rupee, we have x = 1. Substituting this value into the equation, we get:
1 + (1 + 1) + (1 + 3) + ... + (1 + (n-1)) = total amount
Simplifying further, we have:
1 + 2 + 3 + ... + (n-1) = total amount - n + 1
Step 3: Solving the equation
The sum of consecutive numbers from 1 to (n-1) can be calculated using the formula:
Sum = (n-1)(n)/2
Substituting this into the equation, we have:
(n-1)(n)/2 = total amount - n + 1
Since the total amount is 67 rupees, we can substitute it into the equation:
(n-1)(n)/2 = 67 - n + 1
Simplifying further, we get:
n^2 - 3n - 132 = 0
Step 4: Solving the quadratic equation
We can solve the quadratic equation by factoring or using the quadratic formula. Factoring is not possible in this case, so we will use the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
For the given equation, a = 1, b = -3, and c = -132. Substituting these values into the quadratic formula, we get:
n = (-(-3) ± √
Community Answer
A sum is to be distributed among certain number of persons. Second per...
34
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.?
Question Description
A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.?.
A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.?.
Solutions for A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? defined & explained in the simplest way possible. Besides giving the explanation of
A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.?, a detailed solution for A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? has been provided alongside types of A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? theory, EduRev gives you an
ample number of questions to practice A sum is to be distributed among certain number of persons. Second person gets one rupee more than the first, third person gets two rupees more than the second and the fourth person gets three rupees more than the third and so on. If the first person gets one rupee and the last person 67 rupees, find the number of persons.? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup