Question

Rahul drew a rectangular grid of 625 cells, arranged in 25 Rows and 25 columns, and filled each cell with a number. The numbers with which he filled each cell were such that the numbers of each row taken from left to right formed an arithmetic series and the numbers of each column taken from top to bottom also formed an arithmetic series. The 6th and the 20th numbers of the fifth row were 37 and 73 respectively, while the 6th and the 20th numbers of the 25th row were 63 and 87, respectively. What is the sum of all the numbers in the grid?

(a) 32798

(b) 65596

(c) 52900

(d) of these

Answer 1

Correct option (d) of these

Explanation:

It is evident that the whole question is built around Arithmetic progressions. The 5th row has an average of 55, while the 25th row has an average of 75. Since even column wise each column is arranged in an AP we can conclude the following:

1st row - average 51 - total = 25 × 51

2nd row - average 52 - total 25 × 52.....

25th row - average 75 - total 25 × 75

The overall total can be got by using averages as:

25 (51 + 52 + 53 + …..+ 75)= 25.1575 = 39375.