Question

Rs. $3,000$ is divided among A. B and C. such that A receives one-third as much as B and C together receive and B receives $2:3$ as much as A and C together receive. Then share of C is

• A. Rs.$525$
• B. Rs.$1,625$
• C. Rs.$1,050$
• D. Rs. $600$

Answer 1

Answer: (C)

Rs.$1,050$

A = $\frac{1}{3}$ (B + C)
And B = $\frac{2}{3}$ ( A + C)
From (1),
$3A=B+C$
$3A-C=B$
Putting value of B in equation (2),
$\therefore 3A-C$ = $\frac{2}{3}$ (A + C)
$\Rightarrow$ $9A-3C=2A+2C$
$\Rightarrow$ $7A=5C$
$\Rightarrow$ A = $\frac{5}{7}$ C
$\frac{A}{C}=\frac{5}{7}$
$\therefore$ $B=3A-C=3$ $\times \frac{5}{7}$ C-C = $\frac{8}{7}$ C
$\frac{B}{C}=\frac{8}{7}$
Now A : B : C = $5:8:7$
Share of C = $\frac{7}{20}\times$ $3000=Rs.1050.$