Question

During a campaign an army loses 1 10th of its members in battle and 1 5th sickness,what fraction survives

Answer 1

Given :

During a campaign an army loses $\frac{1}{10}$ th of its members in battle and $\frac{1}{5}th$ sickness.

To Find :

The fraction of remaining members of survives.

Solution :

Let the total number of members in army = 1

Fraction of members lost in battle = $\frac{1}{10}th$

Fraction of members are sick = $\frac{1}{5}th$

Fraction of surviving members = $1-(\frac{1}{10} +\frac{1}{5})$

                                                   = $1-(\frac{1+2}{10})$

                                                   = $1-\frac{3}{10}$

                                                   =  $\frac{10-3}{10}$

                                                   =  $\frac{7}{10}$

$\frac{7}{10}$th of its members survive.