Question

The average marks scored by Amit, Bimal and Candy in an examination is 84. If marks of Dorothy are
now added, the average marks of the 4 students becomes 80. Ellora's score is 3 more than Dorothy. If
Ellora's marks replace Amit's marks, than the average marks scored by Bimal, Candy, Dorothy and Ellora
is 79. What is the score of Amit?

Answer 1

Answer:

Score of Amit = 75

Step-by-step explanation:

Let marks of Amit be A, Bimal be B, Candy be C, Dorothy be D and Ellora be E

According to first condition,

The average marks scored by Amit, Bimal and Candy in an examination is 84

That is,

$\frac{A+B+C}{3}$ = 84

A + B + C = 84 * 3

A + B + C = 252

Now,

According to the second condition,

If marks of Dorothy are  added, the average marks of the 4 students becomes 80, that is,

$\frac{A+B+C+D}{4}$ = 80

A + B + C + D = 80 * 4

A + B + C + D = 320

Now substituting value of A + B + C  from above

252 + D = 320

D = 320 - 252

D = 68

So,

Marks of Dorothy = 68

Next in the question , it is given as ,

Ellora's score is 3 more than Dorothy, that is,

Marks of Ellora = Marks of Dorothy + 3

Marks of Ellora = 68 + 3

Marks of Ellora = 71

Finally, it is given

Ellora's marks replace Amit's marks, then the average marks scored by Bimal, Candy, Dorothy and Ellora  is 79, that is

$\frac{B+C+D+E}{4}$ = 79

Substituting value of D = 68 and E = 71

$\frac{B+C+68+71}{4}$ = 79

B + C + 139 = 79 * 4

B + C + 139 = 316

B + C = 316 - 139

B + C = 177

Now, According to first condition we know,  

A + B + C = 252

So, substituting value of B + C = 177 in this equation,

A + 177 = 252

A = 252 - 177

A = 75

Hence,

Score of Amit = 75