if the mode of the given data is 45 find x and y

1 class 10-20 20-30 30-40 40-50 50-60 60-70 70-80 total
2 frequency 4 8 x 12 10 4 y 50

Mode = l + [f - f0/2f - f0 - f1] * h
According to the question : sum of frequencies= 50 
4+8+12+10+4+x+y = 50
x+y= 12 and y = 12-x  - (i)
now, 45 = 40 + (12 -x/24 - x - 10)*10 (mode formula)
5 = (120 - 10x)/(14-x)
(14-x)*5 = 120 - 10x
​70 - 120 = -10x + 5x
​x = -50/-5 = 10
​y = 2 [by (i)]