If the ratio of selected to unselected candidates was 14 : 25. If 35 less had applied and 10 less selected, the ratio of selected to unselected would have been 3 : 5. What is the number of candidates who had applied for a job?

If the ratio of selected to unselected candidates was 14 : 25.

Let's assume the number of selected candidates initially was 14y.

Let's assume the number of unselected candidates initially was 25y.

total number of candidates initially = 14y+25y

= 39y

If 35 less had applied and 10 less selected, the ratio of selected to unselected would have been 3 : 5.

total number of candidates after change = (39y-35)

number of selected candidates after change = (14y-10)

number of unselected candidates after change = (39y-35)-(14y-10)

= 39y-35-14y+10

= (25y-25)

$$\frac{(14y-10)}{(25y-25)}\ =\ \frac{3}{5}$$

$$\frac{(14y-10)}{(5y-5)}\ =\ 3$$

14y-10 = 15y-15

15y-14y = 15-10

y = 5

Number of candidates who had applied for a job = 39y

= $$39\times5$$

= 195