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Linear Equations

Linear Equations

MODULES

Basics of Equations
Graph, Dependent & Inconsistent Equations
Solving Equations
Age, Digits & Fraction Based Questions
Wrong Calculation and Exam Based Questions
Integer Solutions
2 Equations & 3 Variables
Items Measured in Groups of 2 or more
Transposed & Multiple Variables
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Linear Equations 1
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Linear Equations 2
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PRACTICE

Linear Equations : Level 1
Linear Equations : Level 2
Linear Equations : Level 3
ALL MODULES

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

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4.4 Wrong calculation questions

Example 10

A teacher gave a number to Nandini and asked her to multiply it by 161616. However, when she mistakenly multiplied the number by 616161, the teacher noted the difference between this resultant product and the actual product was 840840840 less than five times the actual product. What was the number given to Nandini?

Solution

Let the number given to Nandini be xxx. Therefore, actual product and the incorrect resultant product are 16x16x16x and 61x61x61x respectively.

Difference between resultant product and actual product was 840840840 less than five times the actual product.
⇒ 61x−16x=5×16x−840 61x - 16x = 5 \times 16x - 84061x−16x=5×16x−840
⇒ 35x=840 35x = 84035x=840

⇒ x=84035=24 x = \dfrac{840}{35} = \bm{24}x=35840​=24

Answer: 242424


4.5 Exam-based questions

Example 11

In an examination there are 303030 questions. 111 mark is given for each correct answer and 0.250.250.25 is deducted for every incorrect answer. Ankur attempted all the questions and scored 13.7513.7513.75. How many incorrect answers did he have? [XAT 2009] (111) 101010            (222) 111111            (333) 121212            (444) 151515            (555) None of the above           

Solution

Let the number of correct answers and wrong answers be xxx and yyy respectively. We need to find yyy. As every question was attempted, x+y=30x + y = 30x+y=30 ⇒ x=30−y\bm{x = 30 - y}x=30−y -----(111)

As he scored 111 for correct answer, −0.25-0.25−0.25 for wrong answer and 13.7513.7513.75 marks overall, x×1−0.25×y=13.75x \times 1 - 0.25 \times y = 13.75x×1−0.25×y=13.75

⇒ x−0.25y=13.75 x - 0.25y = 13.75x−0.25y=13.75

⇒ 30−y−0.25y=13.75 30 - y - 0.25y = 13.7530−y−0.25y=13.75 [Substituting Eq (111)]

⇒ 1.25y=16.25 1.25y = 16.251.25y=16.25 ⇒ 54×y=16.25\dfrac{5}{4} \times y = 16.2545​×y=16.25

⇒ y=16.25×45=654=13 \bm{y} = 16.25 \times \dfrac{4}{5} = \dfrac{65}{4} = \bm{13}y=16.25×54​=465​=13

Answer: (555) None of the above


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