### Practice Quant Quiz Set-14 for LIC , SO and railways

Dear Bank Aspirants practice Quant Questions for upcoming LIC Exam, Specialist officer and other exams. Try to solve these Mixed Questions and share time taken to solve these Mixed Questions  and your attempt.

Practice Quant Questions for Bank , Railway and LIC Exam.

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

1.
I. 10p^2 + 39p - 88 = 0
II. 21q^2 + 41q - 40 = 0

2.
I. 14p^2 - 43p + 20 = 0
II. 33q^2 + 72q + 12 = 0

3.
I. 56p^2 + 97p + 42 = 0
II. 99q^2 - 64q + 5 = 0

4.
I. 16p^2 - 40p + 25 = 0
II. 25q^2 - 40q + 16 = 0

5.
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
1. 5
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.

2. 1;
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.

3. 2
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.

4. 1
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.

5. 5
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

7. 1
Suppose the present ages of P and Q are 4k and 5k respectively.
Then,
(4k + 6)/(5k + 6) = 7/8
Sum of the ages of P and Q
= 4k + 5k = 9k
= 9 × 2 = 18 years

8. 3

9. 2

10. 3
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.