Reciprocal Sum Calculation: Math MCQ Solution

Problem Statement

We are asked to find the sum of the reciprocals of two numbers, given their sum and product.

Given Information

• Sum of the two numbers ($a + b$) = 30
• Product of the two numbers ($a \times b$) = 50

Objective

Calculate the sum of the reciprocals of these two numbers, which is represented as $\frac{1}{a} + \frac{1}{b}$.

Solution Steps

1. Represent the sum of reciprocals using a common denominator:

   $ \frac{1}{a} + \frac{1}{b} = \frac{b}{ab} + \frac{a}{ab} = \frac{a+b}{ab} $

2. Substitute the given values for the sum ($a+b$) and the product ($ab$) into the expression:

   $ \text{Sum of reciprocals} = \frac{30}{50} $

3. Simplify the resulting fraction:

   $ \frac{30}{50} = \frac{3 \times 10}{5 \times 10} = \frac{3}{5} $

Final Answer

The sum of the reciprocals of the two numbers is $\frac{3}{5}$.