Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
The ratio of incomes of $A$ and $B$ is 3 : 4. The ratio of their expenditures is 4 : 5. Find the ratio of their savings if the savings of $A$ is one-fourth of his income. (Campus Recruitment, 2008)
Answer
Answer (as printed):
Explanation
Let the incomes of $A$ and $B$ be $3x$ and $4x$ and their expenditures be $4y$ and $5y$ respectively. Then, $A$'s savings $=3x-4y$. $$\therefore \quad 3x-4y=\frac{1}{4}\text{ of }3x \Rightarrow 12x-16y=3x \Rightarrow 9x=16y \Rightarrow y=\frac{9}{16}x.$$ So, ratio of savings $=\frac{A\text{'s savings}}{B\text{'s savings}}=\frac{3x-4y}{4x-5y}=\frac{3x-4\times\frac{9}{16}x}{4x-5\times\frac{9}{16}x}=\frac{3x-\frac{9}{4}x}{4x-\frac{45}{16}x}=\left(\frac{3}{4}x\times\frac{16}{19x}\right)=12:19.$