Let number of 25 paise coins be x and number of 50 paise coins be y.

According to given conditions, we have

x + y = 40 …(1)

and 25x + 50y = 1275 …(2)

Multiplying equation (1) by 50, we get

50x + 50y = 2000 …(3)

Subtracting equation (3) from (2), we get

-25x = - 725 implies x = 29

Substituting x = 29 in equation (1), we get

29 + y = 40 implies y = 11

Hence, number of 25 paise coins = 29 and number of 50 paise coins = 11.