# Solutions

1. 3;a

2. 20x^2 + 45x + 28x + 63 = 0
(5x + 7) (4x + 9) = 0
x = -7/5, 9/4
1. 16y^2 + 12y + 4y + 3 = 0
(4y +1) (4y +3) = 0
y = -1/4, -3/4
x < y

2. 4;
3. x^2 – 15x – 11x + 165 = 0
or, (x – 11) (x – 15) = 0
or, x = 11, 15
1. y2 – 21y – 15y + 315 = 0
or, (y – 15) (y – 21) = 0
or, y = 15, 21
x <= y

3. 1;
4. 3x^2 – 21x – 11x + 77 = 0
or, (3x – 11) (x – 7) = 0
x = 11/3, 7
1. 2y^2 + 16y + 7y + 56 = 0
or, (2y + 7) ( y + 8) = 0
y = -7/2,–8
x > y

4. 5;
5. 63x^2 + 35x + 36x + 20 = 0
(7x +4) (9x + 5) = 0
x = -4/7, -5/9
1. 45y^2 + 27y + 25y + 15 = 0
(9y + 5) (5y + 3) = 0
y = -5/9, -3/5
No relationship between x and y exists

5. 3;
6. x^2 + 9x + 7x + 63 = 0
(x + 7) (x + 9) = 0
x = –7, –9
1. 6y^2 – 24y – 13y + 52 = 0
(6y – 13) ( y – 4 ) = 0
y = 13/6, 4
x < y

6. 2;
Let the total number of pineapple be x
70/100 x = 350
x = 350 * 100/70 = 500

7. 3;
Ratio of their uses = 8 : 10 : 12 = 4 : 5 : 6
Rent paid by R = 6/15 * 2250 = Rs. 900

8. 2;
Part of tank filled in 1 hour
1/20 + 1/24 – 1/40 = 15
Thus, required time for the tank to be filled = 15 hrs.

9. 2;
15 A = 10 B
3A = 2B
Now, B – 10 = 3A – 22
or, B – 10 = 2B – 22 or, (Put 3A = 2B)
or, B = 12
A = 2*12/3 = 8
Required sum = 20

10. 5;
Speed of train = 450/6 = 75 km/hr
Speed of bike = 75/2 = 37.5 km/hr
Time taken by bike = 300/37.5 = 8 hour