Given information:
- Sum of two numbers = 62
- Product of two numbers = 960

Let's assume:
- The two numbers are x and y.

Sum of the two numbers:
- According to the given information, x + y = 62.

Product of the two numbers:
- According to the given information, x * y = 960.

Using the equations:
We can solve the given equations simultaneously to find the values of x and y.

Solving the equations:
1. We can rewrite the equation x + y = 62 as y = 62 - x.
2. Substitute this value of y in the equation x * y = 960:
x * (62 - x) = 960
62x - x^2 = 960
Rearranging the equation: x^2 - 62x + 960 = 0
3. We can now solve this quadratic equation to find the values of x.
By factoring or using the quadratic formula, we find x = 30 and x = 32.
4. Substitute these values of x in the equation y = 62 - x to find the values of y.
For x = 30, y = 62 - 30 = 32.
For x = 32, y = 62 - 32 = 30.

Sum of their reciprocals:
Now, we need to find the sum of the reciprocals of x and y.
The reciprocal of a number is obtained by taking the inverse (1 divided by the number).

1. Reciprocal of x: 1/x
Reciprocal of y: 1/y

2. Sum of reciprocals: (1/x) + (1/y)
For x = 30 and y = 32:
Sum of reciprocals = (1/30) + (1/32)
Simplifying the expression, we get:
Sum of reciprocals = (32 + 30) / (30 * 32)
= 62 / 960
= 31 / 480

Therefore, the sum of the reciprocals of the two numbers is 31/480.