You have to write out the initial fraction of blue and red beads, as well as the fraction of beads after 170 have been given away. Since the no. of blue beads decreases by 40%, it means that 60% of the initial fraction is left. Also, they mention that no. of red beads is 4/5 of the initial number, thus you can calculate the fraction of red beads after 170 have been given away. With the fractions, you will be able to calculate the number of units that represents the 170 beads and thus able to work out how many beads represent 1 unit. Since they ask for the number of beads left, you will have to add up the number of units representing the red and blue beads after beads were taken out (frm the fraction calculated).

Find the ratio of blue to red beads in the end and equate the change in number of units of beads to 170. Find the total number of units of beads and hence, total number of beads.