Consider the following data : | | Average marks in English | Average marks in Hindi | | :--- | :---: | :---: | | Girls | 9 | 8 | | Boys | 8 | 7 | | Overall average marks | 8·8 | x | What is the value of x in the above table?
- (a) 7·8 ✓ UPSC's answer
- (b) 7·6
- (c) 7·4
- (d) 7·2
Why the answer is (a)
• Let the number of girls be $G$ and the number of boys be $B$.
• The overall average in English is given as 8.8, so the total English marks are $9G + 8B = 8.8(G + B)$.
• Solving this equation: $9G + 8B = 8.8G + 8.8B \Rightarrow 0.2G = 0.8B \Rightarrow G = 4B$.
• The overall average in Hindi ($x$) is calculated as $\frac{8G + 7B}{G + B}$.
• Substituting $G = 4B$ into the Hindi average formula: $x = \frac{8(4B) + 7B}{4B + B} = \frac{32B + 7B}{5B} = \frac{39B}{5B} = 7.8$.
• Therefore, the value of $x$ is 7.8, which corresponds to option (a).
Why the other options are wrong
- (b) 7·6
- Option (b) 7.6 is incorrect because the correct calculation yields 7.8.
- (c) 7·4
- Option (c) 7.4 is incorrect because the correct calculation yields 7.8.
- (d) 7·2
- Option (d) 7.2 is incorrect because the correct calculation yields 7.8.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.