Question

A sum of rs. 770 has been divided among a, b, c in such a way that a receives 2/9th of what b and c together receive. then a's share is

Answer 1

a + b + c = 770
a = (2/9) (b + c) => 9a - 2b -2c = 0;
on solving we get b + c = 630
Therefore a = (2/9)*630 = 140

Answer 2

Share of A is 140.

Given:  

A sum of Rs. 770 has been divided between A, B, C

To find:  

Share of A

Solution:

From given,

$\begin{array}{l}{A+B+C=770} \\ {B+C=770-A \rightarrow(1)}\end{array}$

Also given that $A=\frac{2}{9}(B+C)$

$9 A-2(B+C)=0 \rightarrow(2)$

Substitute equation (1) in equation (2)

$\begin{array}{l}{9 A-2(770-A)=0} \\ {9 A-1540+2 A} \\ {9 A=1540-2 A} \\ {11 A=1540} \\ {A=\frac{1540}{11}} \\ {A=140}\end{array}$

Therefore, A's share is 140.