The sum of two numbers is 12 and their product is 35. What is the sum of reciprocals of these numbers?

The sum of two numbers is 12 and their product is 35. What is the sum of reciprocals of these numbers? ?

Created: 1 year ago | Updated: 2 months ago | Created By:

Ashraful Islam

12/35

1/35

35/8

7/32

0 19

Institution: Bangladesh Development Bank Exam: Bangladesh Development Bank Ltd - Officer - 28.03.2014
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we need to find two numbers, let's call them x and y, such that their sum and product meet the conditions given:

1. The sum: \( x + y = 12 \)
2. The product: \( x \times y = 35 \)

We can use these equations to express the numbers in terms of their reciprocals. The sum of the reciprocals of x and y is given by:

\[
\frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy}
\]

Substituting the values we know:

\[
\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} = \frac{12}{35}
\]

This simplification shows that the sum of the reciprocals of the two numbers (x and y) is indeed \(\frac{12}{35}\).

Hence, the correct answer is **A) 12/35**. This result highlights the relationship between the sum and product of two numbers and their reciprocals, a useful concept in algebra that reveals insights into symmetry in equations.

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