GATE Mechanical 2023 | GA | Question: 3

Question

A certain country has $504$ universities and $25951$ colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

 

• A. $22.7$
• B. $23.7$
• C. $15.0$
• D. $66.8$

Comments

Simple Approach : 
$P_{\text{overall}} = P_{\text{colleges}} - \left[ \left( \frac{N_{\text{universities}}}{N_{\text{total}}} \right) \times (P_{\text{colleges}} - P_{\text{universities}}) \right]$  

where as ,
$N_{\text{universities}} = 504$, $P_{\text{universities}} = 7\%$
$N_{\text{colleges}} = 25,951$, $P_{\text{colleges}} = 23\%$

Answer 1

Given that, 

• Number of universities in a country $=504$
• Number of colleges in a country $=25951$

 The number of universities that fall into Grade III $=7\% \text{ of } 504 = \dfrac{7}{100} \times 504 = 35.28$

The number of colleges that fall into Grade III $=23\% \text{ of } 25951 = \dfrac{23}{100} \times 25951 = 5968.73$

Thus, required percentage $=\dfrac{\text{Total number of universities and colleges that fall into grade III}}{\text{Total number of universities and colleges}} \times 100\%$

$= \dfrac{35.28 + 5968.73}{504 + 25951} \times 100\% = \dfrac{6004.01}{26455} \times 100\%$

$= 0.2269518 \times 100\% = 22.69518\% \approx 22.7\%.$

Correct Answer: A