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Algebra

Linear Equations

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CAT 2025 Lesson : Linear Equations - Wrong Calculation and Exam Based Questions

4.4 Wrong calculation questions

Example 10

A teacher gave a number to Nandini and asked her to multiply it by

16

. However, when she mistakenly multiplied the number by

61

, the teacher noted the difference between this resultant product and the actual product was

840

less than five times the actual product. What was the number given to Nandini?

Solution

Let the number given to Nandini be

x

. Therefore, actual product and the incorrect resultant product are

16x

and

61x

respectively.

Difference between resultant product and actual product was

840

less than five times the actual product.
⇒

61x - 16x = 5 \times 16x - 840

⇒

35x = 840

⇒

x = \dfrac{840}{35} = \bm{24}

Answer:

24

4.5 Exam-based questions

Example 11

In an examination there are

30

questions.

1

mark is given for each correct answer and

0.25

is deducted for every incorrect answer. Ankur attempted all the questions and scored

13.75

. How many incorrect answers did he have? [XAT 2009] (

1

)

10

(

2

)

11

(

3

)

12

(

4

)

15

(

5

) None of the above

Solution

Let the number of correct answers and wrong answers be

x

and

y

respectively. We need to find

y

. As every question was attempted,

x + y = 30

⇒

\bm{x = 30 - y}

-----(

1

)

As he scored

1

for correct answer,

-0.25

for wrong answer and

13.75

marks overall,

x \times 1 - 0.25 \times y = 13.75

⇒

x - 0.25y = 13.75

⇒

30 - y - 0.25y = 13.75

[Substituting Eq (

1

)]

⇒

1.25y = 16.25

⇒

\dfrac{5}{4} \times y = 16.25

⇒

\bm{y} = 16.25 \times \dfrac{4}{5} = \dfrac{65}{4} = \bm{13}

Answer: (

5

) None of the above

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