The difference of two unit fractions is one third of their sum. Find ratio of the larger fraction to smaller fraction

Given: The difference of two unit fractions is one-third of their sum

To find: the ratio of the larger fraction to a smaller fraction

Solution:

Let $\frac{1}{a} , \frac{1}{b}$ are the two fractions

$\left(\frac{1}{a}\right)-\left(\frac{1}{b}\right)=\left(\frac{1}{3}\right) \cdot\left(\left(\frac{1}{a}\right)+\left(\frac{1}{b}\right)\right)$

$\left(\frac{3}{a}\right)-\left(\frac{3}{b}\right)=\left(\frac{1}{a}\right)+\left(\frac{1}{b}\right)$

$\left(\frac{2}{a}\right)=\left(\frac{4}{b}\right) \cdots$ ( subtracted 1 / a  and  added  3 / b to both sides)

$\frac{\left(\frac{1}{a}\right)}{\left(\frac{1}{b}\right)}=2$

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

30 Views

Kickstart Your Career

Get certified by completing the course

Get Started