Question
Download Solution PDFComprehension
The following table shows the total number of students who are learning both Chess and Squash in four different colleges, namely, A, B, C and D along with the difference between the number of students learning Chess and Squash and also the percentage of students learning Carrom. Based on the data in the table, answer the questions that follow:
College-wise details of students learning Chess, Squash and Carrom.
| College | Total Number of Students learning Chess and Squash | Difference between the Number Students learning Chess and Squash | Percentage of Students learning Carrom |
| A | 2100 | 300 | 30% |
| B | 1170 | 30 | 35% |
| C | 1260 | 140 | 40% |
| D | 1800 | 400 | 25% |
Note:
(1) Total number of students in a college = Number of Students learning Chess + Number of Students learning Squash + Number of Students learning Carrom.
(2) Every student in a college learns only one of the three games.
(3) Number of students learning Chess is more than the number of students learning Squash in each college.
In College B, if the ratio of the number of boys to girls is 5 : 4 and 30% of the girls are learning Carrom, then what is the number of boys learning Chess and Squash together ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFLet's solve the set by creating a table:
For College A:
Number of chess players + number of squash players = 2100 .....(1)
Number of chess players - number of squash players = 300 .....(2)
Solving equations (1) and (2):
Number of chess players = 1200
number of squash players = 900
Now, for Number of carrom players, since 70% of the total students = 2100,
hence, total students = \(\frac{2100×100}{70}= 3000\).
Number of carrom players = 900.
Similarly, For College B:
Number of chess players + number of squash players = 1170 .....(3)
Number of chess players - number of squash players = 30 .....(4)
Solving equations (3) and (4):
Number of chess players = 600
number of squash players =570
Now, for Number of carrom players, since 65% of the total students = 1170,
hence, total students = \(\frac{1170×100}{65}= 1800\).
Number of carrom players = 630.
Similarly, For College C:
Number of chess players + number of squash players = 1260 .....(5)
Number of chess players - number of squash players = 140 .....(6)
Solving equations (5) and (6):
Number of chess players = 700
number of squash players = 560
Now, for Number of carrom players, since 60% of the total students = 1260,
hence, total students = \(\frac{1260×100}{60}= 2100\).
Number of carrom players = 840.
Similarly, For College D:
Number of chess players + number of squash players = 1800 .....(7)
Number of chess players - number of squash players = 400 .....(8)
Solving equations (7) and (8):
Number of chess players = 1100
number of squash players = 700
Now, for Number of carrom players, since 75% of the total students = 1800,
hence, total students = \(\frac{1800×100}{75}= 2400\).
Number of carrom players = 600.
| College | Number of students learning chess | Number of students learning | Number of students learning carrom |
| A | 1200 | 900 | 900 |
| B | 600 | 570 | 630 |
| C | 700 | 560 | 840 |
| D | 1100 | 700 | 600 |
Number of boys in College B = \(\frac{1800}{9}× 5 = 1000.\)
Number of girls in College B = 1800 - 1000 = 800.
Number of girls learning chess and squash = 0.7× 800= 560.
Number of boys learning chess and squash = 1170 - 560 = 610.