Question

If the incomes of company B in 2012 and 2013 were in the ratio 3 : 4, find the ratio of expenditures of that company in these 2 years?

• A. 48 : 55
• B. 42 : 53
• C. 58 : 45
• D. 45 : 58
• E. None of these

Answer 1

The correct option is D 45 : 58

Income $\Rightarrow 1992:1993=3:4=30:40$
$45=(30-E)\times \frac{100}{E}$
$\frac{45E}{100}=30-E$
$\frac{9E}{20}=30-E$
$9E=600-20E$
$29E=600$
$E=\frac{600}{29}.............1992$
$50=(40-E)\times \frac{100}{E}$
$\frac{50E}{100}=40-E$
$E=2(40-E)$
$E=80-2E$
$3E=80$
$E=\frac{80}{3}$
Ratio $=\left(\frac{600}{29}\right)\left(\frac{80}{3}\right)=\frac{600\times 3}{29\times 80}$
$=\frac{1800}{2320}=\frac{180}{232}=\frac{45}{58}$