Question

A boy gets $3$ marks for each correct sum and loses $2$ marks for each incorrect sum. He does $24$ sums and obtains $37$ marks. What was the number of correct sums?

• A. $20$
• B. $17$
• C. $31$
• D. $19$

Answer 1

The correct option is B $17$

Let the number of correct sums be $x$ and the number of incorrect ones be $y$.

Then,according to the question

$x+y=24$ ....(1)

(he attempted 24 questions in total)

$3x-2y=37$ ..(2)

(he gets 3 marks for correct sum and loses 2 marks for wrong sum)

Multiplying (1) by 2 and adding it to (2).

$2x+2y+3x-2y=48+37$

$5x=85$

$x=17$

From (1),

$17+y=24$

$y=7$

He did 17 correct sums.