Discussion
In a partnership business the monthly investment by three friends for the first six months is in the ratio 3 : 4 : 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.
What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
Answer: D
The ratio is 63 : 86 : 110.
Take the monthly investments as 3, 4 and 5 units. For the second six months they rise by 10%, 15% and 20% of those amounts, to 3.3, 4.6 and 6 units. Since both periods last six months, the yearly totals are proportional to the sums:
\[ \begin{aligned} &3 + 3.3 : 4 + 4.6 : 5 + 6 \\ &= 6.3 : 8.6 : 11 = 63 : 86 : 110 \end{aligned} \]
33 : 46 : 60 is the second half-year alone, and 22 : 23 : 24 and 22 : 33 : 50 do not follow from either period.
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