The incomes of the Companies X and Y in 2010 were in the ratio 3 : 4 respectively. What was the respective… · ABC26GN5808
Subject: General Aptitude · Chapter: Line Graphs
The following line graph gives the percent profit earned by two companies X and Y during the period 2006 - 2011. Study the line graph and answer the questions. Profit or Loss % = ((Income - Expenditure)/Expenditure) x 100
Percentage Profit Earned by Companies X and Y over Given Years
Years
X
Y
2006
40
45
2007
45
35
2008
55
50
2009
50
60
2010
65
50
2011
50
55
Chart drawn from the data printed in the source figure.
The incomes of the Companies X and Y in 2010 were in the ratio 3 : 4 respectively. What was the respective ratio of their expenditures in 2010 ?
(a)7 : 22
(b)14 : 19
(c)15 : 22
(d)27 : 35
(e)33 : 40
Answer
Answer (as printed): C
Explanation
Let the incomes of X and Y in 2010 be ₹ $3 x$ and ₹ $4 x$ respectively and let their expenditures be $E_{1}$ and $E_{2}$ respectively. Then, $\frac{\left(3 x-E_{1}\right)}{E_{1}} \times 100=65$ and $\frac{\left(4 x-E_{2}\right)}{E_{2}} \times 100=50$ $$\begin{aligned} & \Rightarrow \quad \frac{3 x}{E_{1}}-1=\frac{65}{100} \text { and } \frac{4 x}{E_{2}}-1=\frac{50}{100} \\ & \Rightarrow \quad \frac{3 x}{E_{1}}=\left(\frac{13}{20}+1\right) \text { and } \frac{4 x}{E_{2}}=\left(\frac{1}{2}+1\right) \\ & \Rightarrow \quad \frac{3 x}{E_{1}}=\frac{33}{20} \text { and } \frac{4 x}{E_{2}}=\frac{3}{2} \\ & \Rightarrow \quad E_{1}=\frac{60 x}{33}=\frac{20 x}{11} \text { and } E_{2}=\frac{8 x}{3} \\ & \Rightarrow E_{1}: E_{2}=\frac{20 x}{11}: \frac{8 x}{3}=60: 88=15: 22 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.