Question

The average marks of 10 students is 41. If the average marks of the top 6 and bottom 5 rankers are 45 and 36 respectively, how much did ​

Answer 1

Answer:

$\blue{let \: marks \: of \: 6th \: student = x} \\ \blue{Average \: marks \: of \: 10 \: students = 41} \\ \blue{ \frac{Total \: marks \: of \: 10 \: students}{10} = 41 } \\ \blue{ \boxed{Total \: marks \: of \: 10 \: students = 410 } - (i)}\\ \blue{Average \: marks \: of \: top \: 6 \: students = 45} \\ \blue{ \frac{Total \: marks \: of \: top \: 5 \: students + x}{6} = 45 } \\\blue{ \boxed{ Total \: marks \: of \: top \: 5 \: students = 270 - x} - (ii) } \\ \blue{Average \: marks \: of \: bottom \: 5 \: students =36} \\ \blue{ \frac{Total \: marks \: of \: bottom \: 4\: students + x}{5} = 36 } \\\blue{ \boxed{ Total \: marks \: of \:bottom \: 4 \: students = 180 - x} - (iii)} \\ \blue{\mathfrak{\underline{\large{put \: the \:value \: of \: {eq}^{n} \: (ii) \: and \: (iii) \: in \: (i)}}}:} \\ \blue{270 - x + 180 - x = 410} \\ \blue{450 - 2x = 410} \\ \blue{2x = 40} \\ \blue{ \rightarrow{\boxed{ x= 20}}} \\ \blue{\mathfrak{\large{Marks \: of \: 6th \: student = x= 20}}} \\ \blue{\mathfrak{\large{Total \: marks \: of \: top \: 5 \: students = 270 - x = 250}}} \\ \blue{\mathfrak{\large{Total \: marks \: of \:bottom \: 4\: students = 180- x = 160}}} \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$