A Shopkeeper has 660 Kesar Petha and 510 Paan Petha. He wants to arrange them in such a manner that each stack has the same number, and they take the least area of the tray. What is the number of Pethas that can be place in each stack for this purpose?

Understanding the Problem

The shopkeeper has 660 Kesar Petha and 510 Paan Petha. He wants to arrange them in stacks such that each stack has the same number of Pethas, and the arrangement takes the least area of the tray. We need to find the number of Pethas that can be placed in each stack for this purpose.

This problem essentially asks for the greatest common divisor (GCD) of the two numbers, which will give us the largest stack size that can be used to arrange both types of Petha in an optimal manner.

Solving the Problem

Let’s find the GCD of 660 and 510.

We can use the Euclidean algorithm to find the GCD:

1. Divide 660 by 510 and find the remainder: \(660 = 510 \times 1 + 150\)
2. Now, divide 510 by the remainder from the previous step: \(510 = 150 \times 3 + 60\)
3. Continue this process until the remainder is 0: \(150 = 60 \times 2 + 30\) and \(60 = 30 \times 2 + 0\)

The last non-zero remainder is 30, so the GCD of 660 and 510 is 30.

Conclusion

The number of Pethas that can be placed in each stack for this purpose is 30.