Management Aptitude Test 2015 Paper

(b) Let the savings of X, Y and Z be ₹ x, ₹ y and ₹ z, respectively.
  $\begin{array}{ccccc}\mathrm{}\mathbf{Income}& \mathit{x}& \mathit{y}& \mathit{z}& =5:7:9\\ \mathbf{Expenditure}& \mathit{x}& \mathit{y}& \mathit{z}& =6:7:12\end{array}$
Given, X saves 30% of his income,
∵ Income - Expenditure = Savings
∴ 5x - 6y = $\frac{30}{100}$ of 5x
⇒ 5x - 6y = $\frac{3}{2}$x
⇒ 5x - $\frac{3}{2}$x = 6y
⇒ $\frac{10\mathit{x}-3\mathit{x}}{2}$ = 6y
⇒ $\frac{7}{2}$x = 6y
⇒ x = $\frac{6\times 2}{7}\mathit{y}=\frac{12}{7}\mathit{y}$ .........(i)
∴ Savings of X = $\frac{3}{2}\times \frac{12}{7}\mathit{y}=\frac{18}{7}\mathit{y}$
For the person Y, 7x - 7y = Savings
On putting the value of x from Eq. (i), we get
Savings = 7 $\times \frac{12}{7}\mathit{y}$ - 7y = 12y - 7y = 5y
Similarly, for person Z Savings = 9x - 12y
On putting savings value of x from Eq. (i), we get
Savings = 9 $\times \frac{12}{7}\mathit{y}$ - 12y
= $\frac{108\mathit{y}-84\mathit{y}}{7}=\frac{24}{7}\mathit{y}$
∴ Ratio of their savings = X : Y : Z
= $\frac{18}{7}\mathit{y}:5\mathit{y}:\frac{24}{7}\mathit{y}$
= 18y : 35y : 24y = 18 : 35 : 24