In an examination, the success to failure ratio was 5 : 2. Had the number of failures been 14 more, then the success to failure ratio would have been 9 : 5. The total number of candidates who appeared for the examination was:

As per the question $$\dfrac{\text{number of success student}}{\text{number of failed student}}=\dfrac{5}{2}$$
Hence, number of success student $$5k$$ and number of failed student $$=2k$$
so, total number of appeared student $$=5k+2k=7k$$
According to the question's condition,

$$\dfrac{5k-14}{2k+14}=\dfrac{9}{5}$$

Hence, $$25k-70=18k+126$$
$$25k-18k=126+70$$
$$7k=196$$
$$k=\dfrac{196}{7}=28$$
Hence, total number of candidates appeared in the exam $$=7\times k =7\times28=196$$