The average marks obtained by five students A, B, C, D and E is 52 3/5 . If the average marks obtained by A, C and D are 53 2/3

Question

The average marks obtained by five students A, B, C, D and E is \(52\frac{3}{5}\) . If the average marks obtained by A, C and D are \(53\frac{2}{3}\) and the average marks obtained by B, C and E are \(52\frac{2}{3}\) , then the marks obtained by C were

(a) 56 

(b) 53 

(c) 57 

(d) 60

Answer 1

Answer is: (a) 56.

Total marks obtained by A + B + C + D + E = 5×\(52\frac{3}{5}\) = 5× \(\frac{263}{5}\) = 263 … (1)

Total marks obtained by

A + C + D = 3 × \(52\frac{2}{3}\) = 3 × \(\frac{161}{3}\) = 161        …(2) 

Total marks obtained by 

B + C + E = 3 × \(52\frac{2}{3}\) = 3 × \(\frac{158}{3}\) = 158        …(3)

∴ (1) — (2)

⇒ Marks obtained by B + E = 263 – 161 = 102    … (4) 

(3) — (4)

∴ Marks obtained by C = 158 – 102 = 56.