# Quant Test for LIC AAO Prelims Exam Set – 9

Directions(1-5): Compare both the equations and choose a correct option.

1. I.12x^2 – 13x + 3 = 0
II.2y^2 + 7y – 4 = 0

y >= x
x > y
No relation
y > x
x >= y
Option C
I.12x^2 – 13x + 3 = 0
=>12x^2 – 9x – 4x + 3 = 0
=>(4x-3)(3x – 1) = 0
=>x = 1/3,3/4
II.2y^2 + 7y – 4 = 0
=>2y^2 + 8y – y – 4 = 0
=>(2y-1)(y+4) = 0
=>y = -4,1/2
No relation.

2. I.4x + 7y = 209
II.12x – 14y = – 38

x >= y
x > y
y > x
y >= x
No relation
Option E
On solving both the equations, we get
x=y = 19
No relation.

3. I.9x^2 – 45x + 56 =0
II. 4y^2 – 17y + 18 = 0

y >= x
No relation
x >= y
y > x
x > y
Option E
I.9x^2 – 45x + 56 =0
=>9x^2 – 24x – 21x + 56 = 0
=>(3x – 8)(3x- 7) = 0
=>x = 8/3,7/3
II. 4y^2 – 17y + 18 = 0
=>4y^2 – 8y – 9y + 18 = 0
=>(y-2)(4y-9) = 0
=>y = 2,9/4
x>y

4. I.9x^2 -36x + 35 = 0
II.2y^2 – 15y – 17 = 0

No relation
x >= y
x > y
y > x
y >= x
Option A
I.9x^2 -36x + 35 = 0
=>9x^2 – 21x – 15x + 35 = 0
=>(3x- 7)(3x – 5)= 0
=>x = 5/3,7/3
II.2y^2 – 15y – 17 = 0
=>2y^2 – 17y + 2y – 17 =0
=>(y+1)(2y – 17)= 0
=>y = -1,17/2
No relation.

5. I.x^2 – 11x + 24 = 0
II.6y^2 – 101y + 425 =0

y > x
y >= x
x > y
No relation
x >= y
Option A
I.x^2 – 11x + 24 = 0
=>x^2 – 3x – 8x + 24 = 0
=>(x-3)(x-8) = 0
=>x = 3,8
II.6y^2 – 101y + 425 =0
=>6y^2 – 50y – 51y + 425 = 0
=>(2y – 17)(3y – 25) = 0
=>y = 17/2,25/3
y > x

6. A fresh fruit contains 80% of water, when it is placed in sunlight after sometime it contains only 25% of water and now its weight is 44 kg. Find the weight o fresh fruit?
152 kg
170 kg
165 kg
136 kg
142 kg
Option C
Water : pulp
Fresh
=> 4:1
Fry
=>1:3
Multiply ratio of fresh fruit by 3 and 4 unit of dry fruit is 44 kg.
1 unit -> 11 kg
Fresh fruit = 11*15 = 165 kg

7. A solution containing 45 ml of acid and 60 ml of water is completely mixed with another solution E, which contains 7/11 of acid. If the proportion of acid and water in the final mixture is equal, find the quantity of solution E.
68 ml
70 ml
55 ml
40 ml
62 ml
Option C
Let the quantity of solution E be x ml.
Amount of acid in final mixture = (45 + 7x/11) ml
Amount of water in final mixture = (60+4x/11) ml
Now, (45 + 7x/11) = (60+4x/11)
=>x = 55 ml

8. A boat can cover 36 km in still water and the same distance downstream, in 4 hours and 3 hours resp. Find the time taken by the boat to cover 21 km upstream and 48km downstream.
3 hours 10 minutes
4 hours 20 minutes
7 hours 30 minutes
6 hours 15 minutes
5 hours 40 minutes
Option C
Speed of boat in still water = 36/4 = 9 km/hr.
Downstream speed = 36/3 = 12 km/hr.
Speed of the stream = 24 – 18 = 3 km/hr.
Upstream speed of the boat = 9-3 = 6 km/hr.
Time taken = 21/6 + 48/12 = 7 hours 30 minutes

9. A,B and C together started a business with initial investments of Rs.4500, Rs.6000 and Rs. 7500 resp. In this business, A is the main working partner for which he gets 16% of the profit to supervise the business, and rest of the profit is shared among them in the ratio of their investments. Find the profit share of A out of the total profit of Rs.5400.
Rs.1662
Rs.1998
Rs.1850
Rs.1998
Rs.1880
Option D
Respective ratio = 4500:6000:7500 = 3:4:5
Profit of A for being a working partner = 0.16*5400 = Rs.864
Profit of A for his investment = (5400- 864)*3/12 = Rs.1134
Total profit share of A = 864+ 1134 = Rs.1998

10. A baseball team of 9 players is to be selected from a group of 7 male players and 6 female players. In how many ways a team having at most four female players is selected?
477 ways
550 ways
320 ways
400 ways
470 ways
Option E
Total number of ways = 6C4*7C5 + 6C3*7C6 + 6C2*7C7
= 315+140+15 = 470 ways