Solution:
Total balloons = a + b + c + d + e + f + g = 800
7.5% of balloons are painted with both yellow and green but not red color.
e = 7.5% of 800 = 60
Ratio of the number of balloons which are painted with only yellow color and that with only green color is 5:4 respectively.
b : c = 5 : 4
=> b = 5c/4
52% of balloons are painted with red color.
a + d + f + g = 52% of 800
a + d + f + g = 416
800 - b - e - c = 416
800 - (5c/4) - 60 - c = 416
c = 144
b = 5 × 144/4
=> b = 180
26% of balloons are painted with only red color which is twice of number of balloons painted with both red and yellow but not green color.
a = 26% of 800
=> a = 208
d = a/2 = 208/2
=> d = 104
22% of balloons are painted with green color but not yellow color.
f + c = 22% of 800
f + 144 = 176
f = 32
Then, a + d + f + g = 416
208 + 104 + 32 + g = 416
g = 72
Number of balloons painted with only two colors = d + e + f = 104 + 60 + 32 = 196
Therefore, the number of balloons painted with only two colors which are star-shaped = (1 - 3/4) × 196 = 49
