Question : Suresh, Dinesh, and Ramesh became partners in a business by investing money in the ratio of 3 : 6 : 8. If their investments are increased by 5%, 15%, and 20%, respectively, then what will be the ratio of their profits for one year?
Option 1: 7 : 46 : 64
Option 2: 19 : 46 : 64
Option 3: 21 : 46 : 64
Option 4: 35 : 46 : 64
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Correct Answer: 21 : 46 : 64
Solution :
The initial ratio of their investment = 3 : 6 : 8
Let the investment by Suresh be $3x$.
Investment by Dinesh is $6x$.
And, Investment by Ramesh is $8x$.
Now, their investments are increased by 5%, 15%, and 20% respectively.
⇒ Investment by Suresh
= $3x+5\% \text{ of }3x=3x+\frac{5}{100}\times3x=3x+\frac{3x}{20}=\frac{63x}{20}$
Investment by Dinesh
= $6x+15\%\text{ of }6x=6x+\frac{15}{100}\times6x=6x+\frac{18x}{20}=\frac{138x}{20}$
And, Investment by Ramesh
= $8x+20\%\text{ of }8x=8x+\frac{20}{100}\times8x=8x+\frac{32x}{20}=\frac{192x}{20}$
So, Required ratio = $\frac{63x}{20}:\frac{138x}{20}:\frac{192x}{20}=63:138:192=21:46:64$
Hence, the correct answer is 21 : 46 : 64.
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