Question

Let $A:(B+C)=6:7$ and $B:(A+C)=8:9$. If a sum of Rs. $221$ is divided among A, B, C, then the shares of A, B, C (in Rs.) respectively will be

• A. $102,104,15$
• B. $100,106,15$
• C. $104,100,17$
• D. $80,100,41$

Answer 1

The correct option is A $102,104,15$

By hypothesis, $\frac{A}{B+C}=\frac{6}{7}$
or $7A=6(B+C)$
or $7A-6B-6C=0$ ...... (i)
and $\frac{B}{A+C}=\frac{8}{9}$
or $9B=8(A+C)$
or $8A-9B+8C=0$ ....... (ii)
Solving equations (i) and (ii) by cross multiplication, we get
$\frac{A}{-48-54}=\frac{b}{-48-56}=\frac{C}{-63+48}$
or $\frac{A}{=102}=\frac{B}{-104}=\frac{C}{-15}$
or $\frac{A}{102}=\frac{B}{104}=\frac{C}{15}$
$\therefore$ Sum of ratios $=102+104+151=221$
Hence, A, Band C's shares are respectively $Rs.102,Rs.104$ and $Rs.15$.