Q) Tara scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, then Tara would have scored 50 marks. Assuming that Tara attempted all questions, find the total number of questions in the test.

Ans: Let x be the number of questions answered correctly and y be the number of questions answered wrongly,

Therefore, total no. of questions = x + y

From given information, we get 3x – y = 40………… (i)

and 4x – 2y = 50 …………….  (ii)

Let’s multiple equation (i) by 2 and subtract equation (ii), we get

2 (3 x – y) – (4 x – 2 y) = 2 (40)- 50

∴ 6 x – 2 y – 4 x + 2 y = 80 – 50

∴ 2 x = 30

∴ x = 15

by substituting x = 15 in equation (i), we get:

3 x – y = 40

∴ 3 (15) – y = 40

∴ 45 – y = 40

∴ y = 45 – 40 = 5

∴ Total no. of questions = x + y = 15 + 5 = 20

Therefore total no. of questions in the test are 20.

Check: let’s put x = 15 and y = 5 in, equation (i), we get:

3 (15) – (5) = 45 – 5 = 40 … hence verified !

Similarly, from equation (ii), we get: 4(15) – 2(5) = 60 – 10 = 50… hence verified!

Hence, our answer is correct !

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