Question

Amrit , Ajay and Sudhansu has 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 sudhansu has one-fifth as many sweets as Ajay (after Amrit gives half his sweets to Ajay), then what is the ratio of the number of sweets Amrit has to the number of sweets sudhansu has?

• A. $10:3$
• B. $15:4$
• C. $3:2$
• D. There is insufficient information to determine the answer

Answer 1

Answer: (A)

$10:3$

Let the number of sweets Amrit, Ajay and Sudhanshu have (after Amrit gives half his sweets to Ajay) be $x,y,$ and $z$ respectively.

$\therefore \frac{\text{number of sweets Amrit have}}{\text{number of sweets Ajay have}}=\frac{2}{3}$ ..... (Given)

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

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

Given that, sudhansu has one-fifth as many sweets as Ajay

number of sweets Sudhanshu have = number of sweets Ajay have

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

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

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

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

Hence, ratio of the number of sweets Amrit has to the number of sweets sudhansu has is $10:3$.