Question : The ratio of the volume of the two cones is 2 : 3, and the ratio of the radii of their bases is 1 : 2. The ratio of their heights is:

Option 1: 3 : 8

Option 2: 8 : 3

Option 3: 4 : 3

Option 4: 3 : 4

Question : If the ratio of the altitudes of two triangles is 3 : 4 and the ratio of their corresponding areas is 4 : 3, then the ratio of their corresponding lengths of bases is:

Option 1: 1 : 1

Option 2: 16 : 9

Option 3: 1 : 2

Option 4: 2 : 1

Question : A, B, and C started a business with their investments in the ratio 1 : 2 : 4. After 6 months A increased his capital by 50% and B invested twice the amount as before, while C withdrew $\frac{1}{4}$th of his investment. The ratio of their profits at the end of the year was:

Option 1: 10 : 5 : 9

Option 2: 5 : 12 : 14

Option 3: 6 : 9 : 17

Option 4: 5 : 14 : 16

Question : In what ratio does the point T(3,0) divide the segment joining the points S(4,–2) and U(1, 4)?

Option 1: $2:1$

Option 2: $1:2$

Option 3: $2:3$

Option 4: $3:2$

Question : In a business, A and C invested amounts in the ratio 2 : 1, while A and B invested amounts in the ratio 3 : 2. If their total annual profit is Rs. 157300, what is B's share of the profit?

Option 1: Rs. 24200

Option 2: Rs. 48000

Option 3: Rs. 36300

Option 4: Rs. 48400