The mean proportional between $\frac{1}{2}$ and $128$  is:

Find the compounded ratio of 

${\left(a+b\right)}^2:{\left(a-b\right)}^2, \left(a^2-b^2\right) :\left(a^2+b^2\right) \mathrm{and} \left({\mathrm{a}}^4-{\mathrm{b}}^4\right) :{\left(\mathrm{a}+\mathrm{b}\right)}^4$

If $\left(7p+3q\right):\left(3p-2q\right)=43:2$, find $p:q$.

If $a:b=3:5$, find $\left(3a+5b\right):\left(7a-2b\right)$.

The ratio of the shorter sides of a right-angled triangle is $5:12$. If the perimeter of the triangle is $360 \mathrm{cm}$, find the length of the longest side.

The ratio of the pocket money saved by Lokesh and his sister is $5:6$. If the sister saves $₹30$ more, how much more the brother should save in order to keep the ratio of their savings unchanged.

In an examination, the number of those who passed and the number of those who failed were in the ratio $3:1$. Had $8$ more appeared, and $6$ less passed, the ratio of passed to failures would have been $2:1$. Find the number of candidates who appeared.