A library has (2m + 1) books with an average price of Rs. 38. If (n + 2) more books with an average price of Rs. 45 are added, then the average price of all books increases by Rs. 2. If instead, (3n - 2) more books with an average price of Rs. 42 are added, the average price increases by Rs. 1.6. Find the value of (8m - 5n).

Total cost of all (2m + 1) books = 38 × (2m + 1) = Rs. (76m + 38)

Cost of (n + 2) books = 45 × (n + 2) = Rs. (45n + 90)

Cost of (3n - 2) books = 42 × (3n - 2) = Rs. (126n - 84)

ATQ;

76m + 38 + 45n + 90 = (2m + 1 + n + 2) × (38 + 2)

Or, (76m + 45n + 128) = (2m + n + 3) × 40

Or, 76m + 45n + 128 = 80m + 40n + 120

Or, 4m = 5n + 8 .................. (I)

Also,

76m + 38 + 126n - 84 = (38 + 1.6) × (2m + 1 + 3n - 2)

Or, 76m + 126n - 46 = (2m + 3n - 1) × 39.6

Or, 76m + 126n - 46 = 79.2m + 118.8n - 39.6

Or, 3.2m = 7.2n - 6.4 ..............(II)

On multiplying equation (II) by 1.25, we get;

4m = 9n - 8

On using the value of '4m' from equation (I), we get;

5n + 8 = 9n - 8

Or, 4n = 16

So, n = (16/4) = 4

On using the value of 'n' in equation (I), we get;

4m = 5 × 4 + 8

So, m = (28/4) = 7

Therefore, required value of (8m - 5n) = 8 × 7 - 5 × 4 = 56 - 20 = 36

Hence, option a.