c
Suppose two cells have emfs \(\varepsilon_{1}\) and \(\varepsilon_{2}\)

\(\left(\text { also } \varepsilon_{1}>\varepsilon_{2}\right)\)

Potential difference per unit length of the potentiometer wire \(=k\) (say)

When \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are in series and supporteach other then

\(\varepsilon_{1}+\varepsilon_{2}=50\, \times k\)       .....\((i)\)

When \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are in opposite direction

\(\varepsilon_{1}-\varepsilon_{2}=10 \times k\)     ....\((ii)\)

On adding eqn. \((i)\) and eqn. \((ii)\)

\(2 \varepsilon_{1}=60\, k \Rightarrow \varepsilon_{1}=30 \,k\) and \(\varepsilon_{2}=50\, k-30 \,k=20\, k\)

\(\therefore \quad \frac{\varepsilon_{1}}{\varepsilon_{2}}=\frac{30 \,k}{20 \,k}=\frac{3}{2}\)