Question

A sum of Rs. $3690$ is divided among P, Q, R and S such that $\frac{P^{\prime }sshare}{Q^{\prime }sshare}=\frac{Q^{\prime }sshare}{R^{\prime }sshare}=\frac{R^{\prime }sshare}{S^{\prime }sshare}=\frac{4}{5}$. Then Q's share is _________?

• A. Rs. $1250$
• B. Rs. $1000$
• C. Rs. $640$
• D. Rs. $800$

Answer 1

Answer: (D)

Rs. $800$

Let S's share be Rs. x

$\therefore$ R's share $=Rs.\left(\frac{4}{5}x\right)$

Q's share $=Rs.\left(\frac{4}{5}\times \frac{4}{5}x\right)=Rs.\left(\frac{16}{25}x\right)$

P's share $=Rs.\left(\frac{4}{5}\times \frac{16}{25}x\right)=Rs.\left(\frac{64}{125}x\right)$

According to question,
$\frac{64}{125}x+\frac{16}{25}x+\frac{4}{5}x+x=3690$

$\Rightarrow \frac{64x+80x+100x+125x}{125}=3690$

$\Rightarrow 369x=3690\times 125$

$\Rightarrow x=\frac{3690\times 125}{369}=1250$

$\therefore$ Q's share $=Rs.\left(\frac{16}{25}\times 1250\right)=Rs.800.$