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CAT 2019 Slot 1 — QA Question 14

PercentageEasy

Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed for passing the examination is

Answer & solution

  • A

    60

  • B

    80

  • 70

  • D

    75

Solution

Easy

Take total marks as 100x100x. Track Meena's score through the two increases, write the two "fails by / exceeds by" conditions as equations, solve for xx, then express the passing mark as a percentage of the total.

1

Initial and post-review scores. She scores 40%40\%, then this is raised by 50%50\%.

score=40x⇒ post-review=40x+12(40x)=60x\begin{aligned} &\text{score}=40x\\ &\Rightarrow\ \text{post-review}=40x+\tfrac{1}{2}(40x)=60x \end{aligned}
2

Use the two conditions. Post-review falls 3535 short of passing; raising it by a further 20%20\% overshoots passing by 77.

pass=60x+35(fails by 35)⇒ 1.2×60x=pass+7=60x+42(20% more, exceeds by 7)\begin{aligned} &\text{pass}=60x+35\quad\text{(fails by 35)}\\ &\Rightarrow\ 1.2\times60x=\text{pass}+7=60x+42\quad\text{(20\% more, exceeds by 7)} \end{aligned}
3

Solve for xx. Simplify the equation from step 2.

72x=60x+42⇒ 12x=42⇒ x=3.5\begin{aligned} &72x=60x+42\\ &\Rightarrow\ 12x=42\\ &\Rightarrow\ x=3.5 \end{aligned}
4

Convert to a passing percentage. Passing marks over total marks.

pass=60x+35=60(3.5)+35=245total=100x=350⇒ 245350×100=70%\begin{aligned} &\text{pass}=60x+35=60(3.5)+35=245\\ &\text{total}=100x=350\\ &\Rightarrow\ \frac{245}{350}\times100=70\% \end{aligned}
Passing percentage=70%\text{Passing percentage}=70\%
CAT 2019 Slot 1 QA Q14: Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails by 3 — Solution | TheCATExam