In Milton school, the number of students who play Badminton is thrice

Question

In Milton school, the number of students who play Badminton is thrice the number of students who play Tennis. The number of students who play both the sports is thrice the number of students who play only Tennis. If 60 students play both the sports, how many students play only Badminton?

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120

(A) 100
(B) 150
(C) 160
(D) 180
(E) 120

stne · Answer

Let  3x  play Badminton

Let  x  play tennis

60  Play  both  sports , so  ONLY  badminton  3x-60  and  ONLY  tennis  x-60

The number of students who play both the sports is thrice the number of students who play only Tennis.

3(x-60)=60 -> 3x-180 =60  ,  3x=240  ,  x=80

Only Badminton  3*80 -60 = 180

Ans- D

Bunuel  , can you please check , whether the OA is correct, Thank you

Hope it's clear.

Bunuel · Answer

_____________________
Edited the OA. Thank you.

ASR2021 · Answer

Bunuel,
Is Algebra the best way to solve this question? I tried on a matrix, though it took me more than 3 minutes. Looking for more ways to solve this question (rather these types of questions).

unraveled · Answer

Venn Diagram works best here.
t = students who play only tennis
3t = students who play both games
Total tennis playing students = 3t + t = 4t
b = students who play badminton only
Total badminton playing students = b + 3t 
 \implies  b + 3t = 3(4t)
b = 9t

Also, 3t = 60
t = 20
Therefore, b = 9t = 180

Answer D.

MBAB123 · Answer

Let  3x  play Badminton

Let  x  play tennis

60  Play  both  sports , so  ONLY  badminton  3x-60  and  ONLY  tennis  x-60

The number of students who play both the sports is thrice the number of students who play only Tennis.

3(x-60)=60 -> 3x-180 =60  ,  3x=240  ,  x=80

Only Badminton  3*80 -60 = 180

Ans- D

Bunuel,
Is Algebra the best way to solve this question? I tried on a matrix, though it took me more than 3 minutes. Looking for more ways to solve this question (rather these types of questions).

Hey  AnkitSingh2020 , for me personally drawing out a 2*2 matrix works best and I was able to solve this in under a minute using the same approach.

ASR2021 · Answer

Hey AnkitSingh2020 , for me personally drawing out a 2*2 matrix works best and I was able to solve this in under a minute using the same approach. Hi Brian, that's what I thought. Thanks for confirming. Maybe with practice I can get it under 2 mins.

EgmatQuantExpert · Answer

Solution 
  Given:  
 • The number of students who play Badminton is thrice the number of students who play Tennis.
• The number of students who play both the sports is thrice the number of students who play only Tennis.
• The number of students who play both the sports = 60

To find:  
 • The number of students who play only badminton.

Approach and Working:   
 • Let the number of students who play only badminton = b
• Let the number of students who play only tennis = t
• Let the number of students who play both the sports = s

Translating the information given in the question, we get:
 • b + s = 3(t + s)
• s = 3t = 60
 o Thus, t = 20

Substituting the value of t and s in the first equation, we get
 • b + 60 = 3(20 + 60)
• b = 180

Hence the correct answer is Option D

Answer: D

bumpbot · Answer

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In Milton school, the number of students who play Badminton is thrice

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