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Amrit, Ajay and Sudhanshu have some sweets with them. Amrit gives half of his sweets to Ajay then Amrit and Ajay will have sweets in a 2:3 ratio. If Sudhanshu has one-fifth as many as Ajay
(After Amrit gives his sweets to Ajay). Then what is the ratio of the number of sweets Amrit has to the number of sweets Sudhanshu has?

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\frac{1}{3}

\frac{10}{3}

\frac{10}{7}

None

answer is B.

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Detailed Solution

Given,
Ratio of sweets of Amrit and Ajay= 2:3.
Suppose
Number of sweets of Amrit =x
Number of sweets of Ajay =y
Number of sweets of Sudhanshu=z

∴ \frac{number of sweets Amrit h ave}{number of sweets Ajay h ave (after Amrit gives half of his sweets)} = \frac{2}{3} ​ . . (given)

\Rightarrow \frac{\frac{x}{2}}{y + \frac{x}{2}} = \frac{2}{3}

\Rightarrow y = \frac{1}{4} x . . . . . (i)

Given that,
Number of sweets Sudhanshu have =

\frac{1}{5} \times

number of sweets Ajay have after Amrit gives his sweets to Ajay)

\Rightarrow z = \frac{1}{5} (y + \frac{x}{2})

\Rightarrow z = \frac{1}{5} (\frac{x}{4} + \frac{x}{2})

\Rightarrow z = \frac{1}{5} (\frac{3 x}{4})

\Rightarrow \frac{\frac{x}{2}}{z} = \frac{10}{3}

As a result, the number of sweets Amrit has to Sudhanshu’s number of sweets is 10:3.
Option 2 is correct.

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