Study the graph carefully and answer the following questions. Following pie chart shows the percentage distribution of number of players playing various games.
1. If the number of players playing Handball is sum of 80% and 50% of the number of players playing Cricket and Football respectively. Find the number of players playing Handball.
a) 2160
b) 2260
c) 2190
d) 2290
e) 2090
Answer: a) 2160
Number of players playing table tennis = 8% of 8000 = 640
Game Number of players
Table tennis 640
Cricket 1200
Football 2400
Hockey 880
Basketball 2880
80% of number of players playing cricket = 80/100 × 1200 = 960
50% of number of players playing football = 50/100 × 2400 = 1200
Number of players playing handball = 960 + 1200 = 2160
2. What is the difference between the number of players playing table tennis and hockey together to the number of players playing football?
a) 840
b) 850
c) 860
d) 870
e) 880
Answer: e) 880
Number of players playing table tennis = 8% of 8000 = 640
Game | Number of players |
Table tennis | 640 |
Cricket | 1200 |
Football | 2400 |
Hockey | 880 |
Basketball | 2880 |
Number of players playing table tennis and hockey together = 640 + 880 = 1520
Number of players playing football = 2400
Required difference = 2400 – 1520 = 880
3. If the ratio of male and female playing cricket is 3 : 2 and the ratio of female and male playing basketball is 2 : 3. Find the sum of number of male players playing cricket and basketball.
a) 2458
b) 2248
c) 2348
d) 2448
e) 2450
Answer: d) 2448
Number of players playing table tennis = 8% of 8000 = 640
Game | Number of players |
Table tennis | 640 |
Cricket | 1200 |
Football | 2400 |
Hockey | 880 |
Basketball | 2880 |
Number of male players playing cricket
Number of male players playing basketball
Required total = 720 + 1728 = 2448
4. What is the average of number of players playing cricket, football, and basketball?
a) 2160
b) 2260
c) 2250
d) 2360
e) 2420
Answer: a) 2160
Number of players playing table tennis = 8% of 8000 = 640
Game | Number of players |
Table tennis | 640 |
Cricket | 1200 |
Football | 2400 |
Hockey | 880 |
Basketball | 2880 |
Total number of players playing cricket, football and basketball = 1200 + 2400 + 2880
=> 6480
Required average = 6480/3 = 2160
5. What is the ratio of number of players playing hockey with respect to the number of players playing table tennis?
a) 11 : 10
b) 11 : 9
c) 13 : 8
d) 3 : 2
e) 11 : 8
Answer: e) 11 : 8
Number of players playing table tennis = 8% of 8000 = 640
Game | Number of players |
Table tennis | 640 |
Cricket | 1200 |
Football | 2400 |
Hockey | 880 |
Basketball | 2880 |
Required ratio = 880 : 640 = 11 : 8
6. What is the percentage of number of players playing cricket with respect to the number of players playing football?
a) 45%
b) 50%
c) 55%
d) 60%
e) 65%
Answer: b) 50%
Number of players playing table tennis = 8% of 8000 = 640
Game | Number of players |
Table tennis | 640 |
Cricket | 1200 |
Football | 2400 |
Hockey | 880 |
Basketball | 2880 |
Required percentage = 1200/2400 X 100= 50%
In the following question, two equations I and II are given. Solve both the equations carefully and choose the correct option.
7. (I) x2 - 3x - 10 = 0 (II) y2 - 14y + 45 = 0
a) y < x
b) x ≤ y
c) x = y or relationship cannot be established
d) x < y
e) x ≥ y
Answer: b) x ≤ y
(I) x^{2} – 3x – 10 = 0
=> (x + 2)(x – 5) = 0
=> x = -2 or 5
(II) y^{2} – 14y + 45 = 0
=> (y – 5)(y – 9) = 0
=> y = 5 or 9
Hence, x ≤ y
8. (I) 6x2 + 43x + 65 = 0 (II) 6y2 - 35y + 51 = 0
a) y < x
b) x ≤ y
c) x = y or relationship cannot be established
d) x < y
e) x ≥ y
Answer: d) x < y
(I) 6x^{2} + 43x + 65 = 0
=> (6x + 13)(x + 5) = 0
=> x = -2.16 or -5
(II) 6y^{2} – 35y + 51 = 0
=> (6y – 17)(y – 3) = 0
=> y = 2.83 or 3
Hence, x < y
9. I. 20x2 - x - 12 = 0 II. 20y2 + 27y + 9 = 0
a) y < x
b) x ≤ y
c) x = y or relationship cannot be established
d) x < y
e) x ≥ y
Answer: c) x = y or relationship cannot be established
From I, (5x-4)(4x+3) = 0
x = -3/4, 4/5
From II, (4y+3)(5y+3) = 0
y = -3/4, -3/5
-3/4 < -3/5 < 4/5
Since one value of y lies between the two values of x, the relationship cannot be established.
10. I. x2 +39x +374 = 0 II. y2 +15y +26 = 0
a) y < x
b) x ≤ y
c) x = y or relationship cannot be established
d) x < y
e) x ≥ y
Answer: d) x < y
From equation I:
x^{2} +39x +374 = (x + 22)(x + 17)= 0
=> x = -22, -17
From equation II:
y^{2} +15y +26 = (y + 13)(y + 2) = 0
=> y = -13, -2
So, x < y