Q)Jaya scored 40 marks in a test getting 3 marks for each correct answer and losing 1 mark for each incorrect answer., Had 4 marks being awarded for each correct answer and 2 marks were deducted for each incorrect answer then Jaya again would have scored 40 marks. How many questions were there in the Test?
Ans:
Step 1: Let X be the number of questions which are answered correctly
and Y be the number of questions which are answered incorrectly.
Therefore, total no. of questions in the test = X + Y
Step 2: Let’s take 1st case: Jaya gets 40 marks with 3 marks for correct answer and – 1 for incorrect answer.
∵ Marks for 1 correct answer = 3
∴ Marks for X correct answers = 3 (X) = 3 X
Similarly, marks for 1 incorrect answer = – 1
∴ Marks for Y incorrect answer = – 1 (Y) = – Y
Therefore, Jaya’s total marks = Marks for correct answers + Marks for incorrect answers
∴ 40 = 3 X – Y …….. (i)
Step 3: Let’s take 1st case: Jaya gets 40 marks with 4 marks for correct answer and – 2 for incorrect answer.
∵ Marks for 1 correct answer = 4
∴ Marks for X correct answers = 4 (X) = 4 X
Similarly, marks for 1 incorrect answer = – 2
∴ Marks for Y incorrect answer = – 2 (Y) = – 2 Y
Therefore, Jaya’s total marks = Marks for correct answers + Marks for incorrect answers
∴ 40 = 4 X – 2 Y …….. (ii)
Step 4: Let’s solve equations (i) and (ii) and find the values of X and Y.
To solve these we multiply equation (i) by 2 and subtract equation (ii) from it, we get:
(2 x 40) – (40) = 2 (3 X – Y) – (4 X – 2 Y)
80 – 40 = 6 X – 2 Y – 4 X + 2 Y
40 = 2 X
X = 
= 20
By substituting value of X = 20 in equation (i), we get:
40 = 3 X – Y
∴ 40 = 3 (20) – Y
∴ 40 = 60 – Y
∴ Y = 60 – 40 = 20
Step 5: Now we have values of X and Y,
∴ Total number of questions = X + Y
= 20 + 20 = 40
Therefore, total no. of questions in the test are 40.
Check: let’s put X = 20 and Y = 20 in, equation (i), we get: 3 (20) – (20) = 60 – 20 = 40 … This matches with the given condition. hence values of X and Y are correct.
Similarly, from equation (ii), we get: 4(20) – 2(20) = 80 – 40 = 40… This also matches with the given condition. hence values of X and Y are correct.
Since both conditions are satisfied, hence our answer is correct.
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