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In a book with a total of 100 pages numbered from 1 to 100, a person proposed to pay 1 rupee for each page number in arithmetic progression. If he paid only 5 rupees for the first 10 pages, how much does he have to pay for the remaining pages of the book? Additionally, the cost of each page is defined arithmetically, such that page number 1 costs 1 rupee, page number 2 costs 2 rupees, and so on. Furthermore, a special amount has to be paid for the last page of the book, which is 50 rupees. How much does the person have to pay in total?
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In a book with a total of 100 pages numbered from 1 to 100, a person p...
Calculating the Total Cost for the Book:
To calculate the total cost for the book, we need to determine the arithmetic progression that represents the cost of each page.

Calculating the Cost of the First 10 Pages:
Given that the person paid 5 rupees for the first 10 pages, we can set up the following equation:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 5
This simplifies to:
55 = 5
Therefore, the common difference between each page is 1 rupee.

Calculating the Cost of the Remaining Pages:
Since the cost of each page increases arithmetically, we can calculate the cost for each page using the arithmetic progression formula:
Cost = a + (n-1)d
Where:
a = cost of the first page
n = page number
d = common difference (1 rupee in this case)
For the last page (page 100), the cost is 50 rupees. Using the formula:
50 = 1 + (100-1)(1)
50 = 1 + 99
50 = 100
Therefore, the total cost for the book can be calculated by summing up the costs of all pages:
Total Cost = Cost of First 10 Pages + Cost of Remaining Pages
Total Cost = 5 + (11 + 12 + ... + 99 + 100)

Calculating the Total Cost:
To calculate the sum of an arithmetic progression, we can use the formula:
Sum = n/2 [2a + (n-1)d]
Substitute the values into the formula:
Total Cost = 5 + 50/2 [2(1) + (50-1)(1)]
Total Cost = 5 + 25 [2 + 49]
Total Cost = 5 + 25 [51]
Total Cost = 5 + 1275
Total Cost = 1280 rupees
Therefore, the person has to pay a total of 1280 rupees for the entire book.
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In a book with a total of 100 pages numbered from 1 to 100, a person proposed to pay 1 rupee for each page number in arithmetic progression. If he paid only 5 rupees for the first 10 pages, how much does he have to pay for the remaining pages of the book? Additionally, the cost of each page is defined arithmetically, such that page number 1 costs 1 rupee, page number 2 costs 2 rupees, and so on. Furthermore, a special amount has to be paid for the last page of the book, which is 50 rupees. How much does the person have to pay in total?
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In a book with a total of 100 pages numbered from 1 to 100, a person proposed to pay 1 rupee for each page number in arithmetic progression. If he paid only 5 rupees for the first 10 pages, how much does he have to pay for the remaining pages of the book? Additionally, the cost of each page is defined arithmetically, such that page number 1 costs 1 rupee, page number 2 costs 2 rupees, and so on. Furthermore, a special amount has to be paid for the last page of the book, which is 50 rupees. How much does the person have to pay in total? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a book with a total of 100 pages numbered from 1 to 100, a person proposed to pay 1 rupee for each page number in arithmetic progression. If he paid only 5 rupees for the first 10 pages, how much does he have to pay for the remaining pages of the book? Additionally, the cost of each page is defined arithmetically, such that page number 1 costs 1 rupee, page number 2 costs 2 rupees, and so on. Furthermore, a special amount has to be paid for the last page of the book, which is 50 rupees. How much does the person have to pay in total? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a book with a total of 100 pages numbered from 1 to 100, a person proposed to pay 1 rupee for each page number in arithmetic progression. If he paid only 5 rupees for the first 10 pages, how much does he have to pay for the remaining pages of the book? Additionally, the cost of each page is defined arithmetically, such that page number 1 costs 1 rupee, page number 2 costs 2 rupees, and so on. Furthermore, a special amount has to be paid for the last page of the book, which is 50 rupees. How much does the person have to pay in total?.
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