| A, B and C invested capitals in the ratio of 4: 6: 9. At the end of the business term, they received the profit in the ratio of 2: 3: 5. Find the ratio of their time for which they contributed their capitals. |
A) 1: 1: 9
B) 2: 2: 9
C) 10: 10: 9
D) 9: 9: 10
Correct Answer: D
Solution :
| Let required ratio of time be \[{{t}_{1}}:{{t}_{2}}:{{t}_{3}}.\] |
| Then, ratio of investments = Ratio of profits |
| \[4{{t}_{1}}:6{{t}_{2}}:9{{t}_{3}}=2:3:5\] |
| Taking first two terms of the ratio, |
| \[\frac{4{{t}_{1}}}{6{{t}_{2}}}=\frac{2}{3}\]\[\Rightarrow \]\[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{1}{1}=\frac{9}{9}\] |
| \[\Rightarrow \] \[{{t}_{1}}:{{t}_{2}}=9:9\] |
| Taking last two terms of the ratio, |
| \[\frac{6{{t}_{2}}}{9{{t}_{2}}}=\frac{3}{5}\]\[\Rightarrow \]\[\frac{{{t}_{2}}}{{{t}_{3}}}=\frac{9}{10}\] |
| \[\Rightarrow \] \[{{t}_{2}}:{{t}_{3}}=9:10\] |
| \[\therefore \] \[{{t}_{1}}:{{t}_{2}}:{{t}_{3}}=9:9:10\] |
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