Question

In one country a part of the residents can speak English only, a part can speak French only and the rest can speak both languages. It is known that $85\%$ residents can speak English, $75\%$ can speak French. What percent of the residents of this country can speak both English and French.

• A. $50\%$
• B. $25\%$
• C. $60\%$
• D. $40\%$

Answer 1

Answer: (C)

$60\%$

$\text{Number of people speaking only English = a}$

$\text{Number of people speaking only French = b}$

$\text{Number of people speaking both languages =}c$

$a+c=\frac{85}{100}(a+b+c)$

$\Rightarrow 20a+20c=17a+17b+17c$

$\Rightarrow 3a+3c=17b-\left(i\right)$

$b+c=\frac{75}{100}(a+b+c$

$\Rightarrow 4b+4c=3a+3b+3c$

$\Rightarrow b+c=3a-\left(ii\right)$

$solvingequation\left(i\right)and\left(ii\right)$

$17b-3a+3a-b=3c+c$

$16b=4c\Rightarrow b=\frac{c}{4}$

Required Percentage of people who can speak both English and French is given by

$(\frac{c}{a+b+c}\times 100)\%$

$=(\frac{c}{\frac{17}{3}b+b}\times 100)\%.\{\text{since}a+c=\frac{17}{3}b\}$

$=(\frac{3c}{20b}\times 100)\%.$

$=(\frac{3c}{20c}\times 4\times 100)\%.\{\because b=\frac{c}{4}\}$

$=60\%$

Answer: option (c)