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CAT 2020 Slot 3 — QA Question 16

PercentageEasy

In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

Answer & solution

  • 399

  • B

    439

  • C

    417

  • D

    357

Solution

Medium

Write everyone's marks as a percentage of the maximum. The gap between Asha and Bishnu, expressed two ways (via Ramesh, and via their percentages), gives one equation; Geeta's marks are then a clean multiple of it.

1

Marks in terms of the maximum. Let the maximum be 100x100x.

Bishnu=52x,Asha=64x,Geeta=84x\begin{aligned} &\text{Bishnu}=52x,\qquad \text{Asha}=64x,\qquad \text{Geeta}=84x \end{aligned}
2

Relate Asha and Bishnu through Ramesh. Bishnu == Ramesh −23-23 and Asha == Ramesh +34+34, so their difference removes Ramesh.

Asha−Bishnu=34−(−23)=57⇒ 64x−52x=57⇒ 12x=57\begin{aligned} &\text{Asha}-\text{Bishnu}=34-(-23)=57\\ &\Rightarrow\ 64x-52x=57\\ &\Rightarrow\ 12x=57 \end{aligned}
3

Geeta's marks. Note 84x=7×12x84x=7\times 12x, using the result of step 2.

Geeta=84x=7×12x=7×57=399\begin{aligned} &\text{Geeta}=84x=7\times 12x=7\times 57=399 \end{aligned}
Geeta=399\text{Geeta}=399
CAT 2020 Slot 3 QA Q16: In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and — Solution | TheCATExam