Question

Krishna has certain number of coins numbered with a series of consecutive natural numbers starting with 1. He found that the sum of squares of all the numbers on the coins is 1753 times the sum of numbers on coins. How many coins does he have?

• A. 1753
• B. 2569
• C. 2629
• D. 3439
• E. 5259

Answer 1

The Correct Option is C

The correct answer is option (C):

2629

Let 'n' be the number of coins Krishna has. The coins are numbered from 1 to n.

The sum of the numbers on the coins is given by the formula for the sum of an arithmetic series:

Sum of numbers = n(n+1)/2

The sum of the squares of the numbers on the coins is given by the formula:

Sum of squares = n(n+1)(2n+1)/6

The problem states that the sum of squares is 1753 times the sum of the numbers. Therefore:

n(n+1)(2n+1)/6 = 1753 * n(n+1)/2

We can divide both sides by n(n+1), assuming n is not 0 (which it cannot be, as he has a certain number of coins). This simplifies the equation to:

(2n+1)/6 = 1753/2

Multiply both sides by 6:

2n + 1 = 1753 * 3

2n + 1 = 5259

Subtract 1 from both sides:

2n = 5258

Divide both sides by 2:

n = 2629

Therefore, Krishna has 2629 coins.