What is the ratio of the number of students learning Chess in College A and B together to the number of students learning Carrom in College D?
- AOption (a)
2 : 5
- BOption (b)
4 : 3
- COption (c)
3 : 1
- DOption (d)
4 : 5
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Correct answer
3 : 1
Why this answer is correct
Let'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 = \(\frac{2100\times100}{70}= 3000\).
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 = \(\frac{1170\times100}{65}= 1800\).
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 = \(\frac{1260\times100}{60}= 2100\).
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 = \(\frac{1800\times100}{75}= 2400\).
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 |
Required ratio: \(\frac{1200+600}{600}= \frac{3}{1}\).