Numbers with H.C.F. 15 must contain 15 as a factor. Now, multiples of 15 between 40 and 100 are 45, 60, 75 and 90. ∴ Number-pairs with H.C.F. 15 are (45, 60), (45, 75), $(60,75)$ and (75, 90). [ $\because$ H.C.F. of $(60,90)$ is 30 and that of $(45,90)$ is 45 ] Clearly, there are 4 such pairs.
Explanation as extracted from the printed page; notation may be imperfect.