Question

Divide Rs $1100$ among A,B and C so that A shall receive $\dfrac{3}{7}$ of what B and C together receive and B may receive $\dfrac{2}{9}$ of what A and C receive ?

Answer 1

Hint: We have to divide rupee 1100 among A,B and C and solve according to the condition given in the question i.e A receive $\dfrac{3}{7}$ of what B and C together receive and B receive $\dfrac{2}{9}$ of what A and C receive . Let assume that the money received by A be x ,by B be y and by C be z .

Complete step-by-step solution:
let the money received by A be x ,by B be y and by C be z
 $x + y + z = 1100$ ……(i)
Given in the question that A receive $\dfrac{3}{7}$ of what Band C together receive
$x = \dfrac{3}{7}(y + z)$
Cross multiplication
$\dfrac{{7x}}{3} = y + z$
From equation(i) $y + z = 1100 - x$
$\dfrac{{7x}}{3} = 1100 - x$
$\Rightarrow \dfrac{{7x}}{3} + x = 1100$
$\Rightarrow \dfrac{{7x + 3x}}{3} = 1100$
$\Rightarrow 10x = 3300$
$\Rightarrow x = \dfrac{{3300}}{{10}}$
$\Rightarrow x = 330$
The money received by A is Rs. 330
Second condition
B receive $\dfrac{2}{9}$ of what A and C receive
$x + z = \dfrac{{9y}}{2}$
From equation(i) $x + z = 1100 - y$
$\dfrac{{9y}}{2} = 1100 - y$
$\Rightarrow \dfrac{{9y}}{2} + y = 1100$
$\Rightarrow \dfrac{{9y + 2y}}{2} = 1100$
$\Rightarrow 11y = 2200$
$\Rightarrow y = \dfrac{{2200}}{{11}}$
$\Rightarrow y = 200$
Substituting value of x and y in equation (i) to get value of z
 $330 + 200 + z = 1100$
 $\Rightarrow z = 1100 - 530$
 $\Rightarrow z = 570$
Hence the shares of A,B and C are respectively $x=330, y=200, z=570$.

Note: Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b. use the concept of ratio and proportion such as in business while dealing with money for many more reasons . Proportion is an equation which defines that the two given ratios are equivalent to each other. The ratio is the number which can be used to express one quantity as a fraction of the other ones.