Question

in an examination one mark is awarded for every correct answer and 1 by half marks deducted for every wrong answer .a candidate answered 80 questions and got 60 marks .how many questions did answer correctly ​

Answer 1

Answer:

66

Step-by-step explanation:

let X question answered right and Y questions answered wrong

given, X + Y = 80. equation (1)

and X*1 - Y * (1/2) = 60

2X - Y = 120. equation (2)

adding equation 1 and 2

3X = 200

X = 200 /3

X = 66.6

Answer 2

Question:

In an examination 1 mark is awarded for every correct answer and 1 $\frac{1}{2}$ marks deducted for every wrong answer. A candidate answered 80 questions and got 60 marks. How many questions did he answer correctly ?

Answer:

The candidate correctly answered 72 questions.

Given:

1 mark is awarded for each correct answer.

1$\frac{1}{2}$ marks is deducted for each wrong answer.

80 questions were answered by the candidate.

The candidate got 60 marks.

To find:

The number of questions answered correctly by the candidate.

Explanation:

Let, the candidate answered 'n' questions correctly.

∴ He wrongly answered = (80-n) question.

For answering correctly he awarded (1×n) marks

                                                             = n marks.

For answering wrongly his mark was deducted by_

(80-n) × 1$\frac{1}{2}$

= (80-n) × $\frac{3}{2}$

$=( \frac{240-3n}{2})$ marks

According to the problem:

n - $(\frac{240-3n}{2} )$ = 60

⇒ $(\frac{2n-240+3n}{2})$ = 60 [∵ The L.C.M. of the denominators is 2]

⇒ 5n-240 = (60×2)

⇒ 5n = 120+240

⇒ n = 360/5

⇒ n = 72

∴ He correctly answered 72 questions.