Question

2. In a mathematics paper there are 10 problems. Each correct answer carries 5 marks whereas for each incorrect answer 2 marks are deducted from the marks scored. Abdul answered all the questions but got only 29 marks. Find the number of correct answers given by Abdul. ----​

Answer 1

Given :-

• Total number of problems in the test = 10
• Total marks given for each correct answer = 5
• Total marks deducted for each incorrect answer = 2
• Total marks scored by Abdul = 29

To Find :-

• Total number of correct answers given by Abdul.

Solution :-

Let x be the total number of correct answers given by Abdul. Then the total number of incorrect answers given by Abdul will be 10 - x (beacuse he attempted all the 10 problems).

According to the question,

⇒ 5x - 2(10 - x) = 29

⇒ 5x - 20 + 2x = 29

⇒ 7x = 29 + 20

⇒ 7x = 49

⇒ x = 49/7

⇒ x = 7

Therefore,

• The number of correct answers given by Abdul = 7

ADDITIONAL INFORMATION:

Total Number of incorrect answers given:-

⇒ 10 - x

Putting the value of x, we get,

⇒ 10 - 7

⇒ 3

Hence, Abdul gave 7 correct answers and 3 incorrect answers in the mathematics test.