Question

Priyanka thinks of a number. She adds 1 to get a second number. She than adds 2 to the 2nd number to get 3rd number, adds 3 to 3rd number to get 4th number and finally adds 4 to the 4th number to get 5th number. Priyanka's brother Bhushan also thinks of a number. But he subtracts 1 to get the 2nd number, He then subtracts 2 from the 2nd number to get the 3rd number and so on till he gets his five numbers. They discover that the sum of Priyanka's five numbers is same as the sum of Bhushan's five numbers. What is the difference between the two numbers of which they first thought?

Answer 1

Answer:

8.

Step-by-step explanation:

Let Pryanka think of number x:

x, x + 1, x +3, x + 6, x + 10     =   5x + 20

His brother thinks of y:

y, x - 1, y - 3, y - 6, y - 10.       = 5y  - 20

The sums are the same, therefore:

5x + 20 = 5y - 20

5x - 5y = -40

(x - y) = -8

y - x = 8.