Directions: In the following questions two equations I and II are given. You have to solve both the equations and give answer :
1) if p > q
2) if p < q
3) if p <= q
4) if p >= q
5) if p = q or the relationship can't be determined
I. 10p^2 + 39p - 88 = 0
II. 21q^2 + 41q - 40 = 0
I. 14p^2 - 43p + 20 = 0
II. 33q^2 + 72q + 12 = 0
I. 56p^2 + 97p + 42 = 0
II. 99q^2 - 64q + 5 = 0
I. 16p^2 - 40p + 25 = 0
II. 25q^2 - 40q + 16 = 0
I. 15p^2 + 38p + 24 = 0
II. 20q^2 + 49q + 30 = 0
6. A mixture of milk and water contains 7% water. What quantity of pure milk should be added to 12 litres of mixture to reduce water to 4%?
1) 5 litres
2) 6 litres
3) 7 litres
4) 8 litres
5) None of these
7. Present ages of P and Q are in the ratio 4 : 5 respectively. Six years hence the ratio becomes 7 : 8. What is the sum of the present ages of P and Q?
1) 18 years
2) 30 years
3) 36 years
4) Can't be determined
5) None of these
8. A started a business investing Rs 10,000. B joined him after six months with an amount of Rs 8,000 and C joined them with Rs 12,000 after another six months. The amount of profit earned should be distributed in what ratio among A, B and C respectively, four years after A started the business?
1) 9 : 7 : 10
2) 10 : 9 : 7
3) 10 : 7 : 9
4) Can't be determined
5) None of these
9. A man bought some fruits at the rate of 4 for Rs 5 and sold them at the rate of 7 for Rs 8. What is the profit/loss per cent?
1) 8 4/7% profit
2) 8 4/7% loss
3) 9 3/8% profit
4) 9 3/8% loss
5) None of these
10. A, B and C can do a piece of work in 20, 30 and 100 days respectively. If A worked alone on the first day, B worked alone on the second day, C worked alone on the third day, A worked alone on the fourth day, and so on, then in how many days the work got completed?
1) 29 days
2) 28 days
3) 31 1/2 days
4) Can't be determined
5) None of these
Answers:
I. 10p^2 + 39p - 88 = 0
or, 10p^2 - 16p + 55p - 88 = 0
or, 2p(5p - 8) + 11(5p - 8) = 0
or, (2p + 11) (5p - 8) = 0
p = -11/2 or 8/5
II. 21q^2 + 41q - 40 = 0
or, 21q^2 + 56q - 15q - 40 = 0
or, 7q(3q + 8) - 5(3q + 8) = 0
or, (7q - 5) (3q + 8) = 0
q = 5/7 or -8/3
We can't get specific relationship between p and q.
I. 14p^2 - 43p + 20 = 0
or, 14p^2 - 35p - 8p + 20 = 0
or, 7p(2p - 5) - 4(2p - 5) = 0
or, (7p - 4) (2p - 5) = 0
p = 4/7 or 5/2
II. 33q^2 + 72q + 12 = 0
or, 33q^2 + 6q + 66q + 12 = 0
or, 3q(11q + 2) + 6(11q + 2) = 0
or, (3q + 6) (11q + 2) = 0
q = -2 or -2/11
Hence, p > q.
I. 56p^2 + 97p + 42 = 0
56p^2 + 49p + 48p + 42 = 0
or, 7p(8p + 7) + 6(8p + 7) = 0
or, (7p + 6) (8p + 7) = 0
p = -6/7 or -7/8
II. 99q^2 - 64q + 5 = 0
or, 99q2 - 9q - 55q + 5 = 0
or, 9q (11q - 1) - 5(11q - 1) = 0
or, (9q - 5) (11q - 1) = 0
or, (9q - 5) (11q - 1) = 0
q = 5/9 or 1/11
Hence, p < q.
I. 16p^2 - 40p + 25 = 0
or, 16p^2 - 20p - 20p + 25 = 0
or, 4p(4p - 5) - 5(4p - 5) = 0
or, (4p - 5) (4p - 5) = 0
p = 5/4, 5/4
II. 25q^2 - 40q + 16 = 0
or, 25q^2 - 20q - 20q + 16 = 0
or, 5q(5q - 4) - 4(5q - 4) = 0
or, (5q - 4) (5q - 4) = 0
q = 4/5, 4/5
Hence, p > q.
I. 15p^2 + 38p + 24 = 0
or, 15p2 + 20p + 18p + 24 = 0
or, 5p(3p + 4) + 6(3p + 4) = 0
or, (5p + 6) (3p + 4) = 0
p = -6/5 or -4/3
II. 20q^2 + 49q + 30 = 0
or, 20q^2 + 24q + 25q + 30 = 0
or, 4q(5q + 6) + 5(5q + 6) = 0
or, (4q + 5) (5q + 6) = 0
q = -5/4 or -6/5
Hence, we can't get any specific relationship between p and q.
6. 5; The quantity of pure milk to be added
= {12 * (7 - 4)}/4 = 9 litres
Suppose the present ages of P and Q are 4k and 5k respectively.
(4k + 6)/(5k + 6) = 7/8
Sum of the ages of P and Q
= 4k + 5k = 9k
= 9 × 2 = 18 years
A's, B's and C's 1 day work = 1/20 + 1/30 + 1/100
Total 3 day's work = 28/300
Total 30 day work = 280/300
Remaining work = 20/300 = 1/15
Now A's 1 day work = 1/20
Then remaining work = (1/60)/(1/30) = 1/2
Now, B's then B complet the remaining work in 1/2
Total number of days = 31 1/2 days.
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