There is a certain pair of numbers such that the sun of twice the first number and thrice the second number is 61. However, when we subtract five times the second number from four times the first number, the answer is 45. Find the second number?

None of these

Let's denote the first number as x and the second number as y.

Given equations:

1. 2x + 3y = 61

2. 4x - 5y = 45

We can solve these equations using substitution or elimination. Let's use elimination.

Multiplying equation 1 by 2:

4x + 6y = 122

Now subtracting equation 2 from this:

(4x + 6y) - (4x - 5y) = 122 - 45

11y = 77

y = 7