Question

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

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

Answer 1

Answer: (A)

$102,104,15$

$\frac{A}{B+C}=\frac{6}{7}--------\left(1\right)$

$\frac{B}{A+C}=\frac{8}{9}--------\left(2\right)$

and $A+B+C=221--------\left(3\right)$

from(1), $7A=6B+6C$

$⟹C=\frac{7A-6B}{6}$

From (2), $\frac{B}{A+C}=\frac{8}{9}$

$9B=8A+8C$

$9B=8A+8\left(\frac{7A-6B}{6}\right)$

$⟹54B=48A+56A-48B$

$102B=104A$

$B=\frac{104A}{102}$

$⟹C=\frac{15A}{102}$

From (3)

$A+\frac{104A}{102}+\frac{15A}{102}=221$

$⟹A=102,B=104,C=15$