Management Aptitude Test 2015 Paper

(b) Let the savings of X, Y and Z be ₹ x, ₹ y and ₹ z, respectively.   $\begin{array}{c c c c c} \text{boIncome} & x & y & z & = 5:7:9 \\ \text{boExpenditure} & x & y & z & =6:7:12 \end{array}$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 ⇒ $\frac{10x-3x}{2}$ = 6y ⇒ $\frac{7}{2}$x = 6y ⇒ x = $\frac{6 \times 2}{7y} = \frac{12}{7y}$ .........(i) ∴ Savings of X = $\frac{3}{2} \times \frac{12}{7} y = \frac{18}{7} y$ For the person Y, 7x - 7y = Savings On putting the value of x from Eq. (i), we get Savings = 7 $\times \frac{12}{7} y$ - 7y = 12y - 7y = 5ySimilarly, for person Z Savings = 9x - 12y On putting savings value of x from Eq. (i), we get Savings = 9 $\times \frac{12}{7} y$ - 12y = $\frac{108y-84y}{7} = \frac{24}{7} y$∴ Ratio of their savings = X : Y : Z = $\frac{18}{7} y : 5y : \frac{24}{7} y$ = 18y : 35y : 24y = 18 : 35 : 24