Question : Given that the ratio of the altitude of two triangles is 4 : 5, the ratio of their areas is 3 : 2, the ratio of their corresponding bases is:

Option 1: 8 : 15

Option 2: 15 : 8

Option 3: 5 : 8

Option 4: 8 : 5

Question : The third proportional of $a$ and $\frac{b^4}{4a}$ is:

Option 1: $\frac{b^8}{16 a^2}$

Option 2: $\frac{b^8}{8 a^2}$

Option 3: $\frac{b^8}{8 a^3}$

Option 4: $\frac{b^8}{16 a^3}$

Question : A, B, and C invested capital in the ratio of 3 : 4 : 8. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. What is the ratio of their invested time?

Option 1: 15 : 16 : 13

Option 2: 13 : 18 : 15

Option 3: 16 : 18 : 15

Option 4: 16 : 21 : 18

Question : The mean proportional of 6 and 54 is _______ more than 15.

Option 1: 3

Option 2: 6

Option 3: 4

Option 4: 5

Question : The value of $15 \div 8-\frac{5}{4}$ of $\left(\frac{8}{3} \times \frac{9}{16}\right)+\left(\frac{9}{8} \times \frac{3}{4}\right)-\left(\frac{5}{32} \div \frac{5}{7}\right)+\frac{3}{8}$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3