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A sum of money is to be distributed among $\text{P, Q, R,}$ and $\text{S}$ in the proportion $5:2:4:3,$ respectively.

If $\text{R}$ gets  ₹ $1000$ more than $\text{S},$ what is the share of $\text{Q (in ₹)}?$

1. $500$
2. $1000$
3. $1500$
4. $2000$

Given that, $\text{P: Q : R : S} = 5:2:4:3$

Let,

• $\text{P} = 5k$
• $\text{Q} = 2k$
• $\text{R} = 4k$
• $\text{S} = 3k$

Now, $\text{R} = \text{S} + 1000$

$\Rightarrow 4k = 3k + 1000$

$\Rightarrow {\color{Blue}{\boxed{k = 1000}}}$

$\therefore$ The share of $\text{Q} = 2k = 2(1000) = \text{₹}\;2000.$

$\textbf{Short Method:}\; \text{P: Q : R : S} = 5:2:\underbrace{4:3}_{1}$

Now,

• $1 \longrightarrow \text{₹}\;1000$
• $2 \longrightarrow \text{₹}\;2000$

Correct Answer $:\text{D}$

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