A can do a work in $7\frac{1}{2}$ hours and B can do the same work in $10\frac{1}{2}$ hours. If they work together for $3\frac{1}{2}$ hours, then what part of the work will be left out ?

$\frac{1}{5}$

A = \( {7 }_{2 }^{1 } \) hours = \(\frac{15}{2}\) hours,

B = \( {10 }_{2 }^{1 } \) hours = \(\frac{21}{2}\) hours,

⇒ A + B worked for \( {3 }_{2 }^{1 } \) hours = (14 + 10) x \( {3 }_{2 }^{1 } \) = 84 units,

⇒ Fraction of work left = \(\frac{105 - 84}{105}\) = \(\frac{21}{105}\) = \(\frac{1}{5}\)