# Quant Test for NIACL 2018 Prelim Exam Set – 8

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

x=y or relation cannot be established.
y>=x
x>y
y>x
x>=y
Option A
4x + 7y = 209] × 2
8x + 14y = 418
12x – 14y = – 38
20x = 380
x = 19
y = 19
x = y

2. I. 6 y^2 + 1/2 = 7/2y
II. 12 x^2 + 2 = 10x

x>=y
y>x
y>=x
x>y
x=y or relation cannot be established.
Option D
6y^2 + 1/2 = 7/2y
12y^2 – 7 y + 1 = 0
12y^2 – 4y – 3y + 1 = 0
4y (3y – 1) – 1 (3y –1) = 0
(3y – 1) (4y – 1) = 0
y = 1/3, 1/4
12x^2 – 10x + 2 = 0
6x^2 – 5x + 1 = 0
3x (2x –1) – 1 (2x –1) = 0
x = 1/3, 1/2
x>y

3. I. 4 x^2 = 49
II. 9 y^2 – 66 y + 121 = 0

x>y
y>=x
y>x
x>=y
x=y or relation cannot be established.
Option E
4x^2 = 49
x^2 = 49/4 = + 7, -7
9y^2 – 66y + 121 = 0
9y^2 – 33y – 33y + 121 = 0
3y (3y – 11) – 11 (3y – 11) = 0
y = 11/3, 11/3

4. I. 6 x + 5 y = 30 xy
II. 5 x + 6 y = 35 xy

y>=x
x>y
x>=y
y>x
x=y or relation cannot be established.
Option D
6/y + 5/x = 30] × 6 5/y + 6/x = 35 ] × 5
36/y+ 30/x = 180
25/y + 30/x = 175
x = 11/60,y = 11/5
x < y

5. I. 6 x^2 – 25 x + 25 = 0
II. 15 y^2 – 16 y + 4 = 0

x=y or relation cannot be established.
x>=y
y>=x
y>x
x>y
Option E
x = 10/6, 15/6
y = 6/15, 10/15
x > y

6. Train A, travelling at 84 kmph, overtook train B, traveling in the same direction, in 10 seconds. If train B had been traveling at twice its speed, then train A would have taken 22.5 seconds to overtake it. Find the length of train B, given that it is half the length of train A.
40 m
80 m
50 m
70 m
60 m
Option C
Let speed of train B be x m/s And length of train B be y m.
Then length of train A is 2y m.
Speed of train A = 84*5/18 = 210/9 = 70/3 m/s.
A.T.Q, (2y+y)/10 = 70/3 – x —–(1)
(2y+y)/22.5 = 70/3 – x —–(2)
From (1) and (2), we get Y = 50 m

7. A contractor employed 25 labourers on a job. He was paid Rs. 275 for the work. After retaining 20 per cent of this sum, he distributed the remaining amount amongst the labourers. If the number of men to women labourers was in the ratio 2 : 3 and their wages in the ratio 5 : 4, what wages did a woman labourer get?
Rs. 9
Rs. 5
Rs. 11
Rs. 8
Rs. 10
Option D
Amount to be distributed amongst labourers
= 275*80/100 = Rs.220
Now, total wages of men : total wages of women = 2 * 5 : 3 *4
= 10:12
Total wages of women = (220*12)22 = Rs.120
Ratio of men to women = 2 : 3
Women = 3/5* 25 = 15
So, each women will get
= 120/15 = Rs. 8

8. A sum of money at simple interest amounts to Rs. 14160 in 3 year. If the rate of interest is increased by 25%, the same sum amount to Rs. 14700 in the same time. Find the rate of interest.
6%
8%
5%
12%
10%
Option A
14160 = P + (P × R × 3)/100
= 3 P R/100 = 14160 – P
=> 14700 = P + (P ×1.25R × 3)/ 100
=> P + 5/ 4 × 3 P R/100 = 14700
=> P + 5/ 4 (14160 − P) = 14700
=> 4 P + 70800 – 5 P = 58800
=> P = 12000 => 14160 = 12000 + (12000 × R × 3)/100
=>14160 = 12000 + 120 × R × 3
=> 14160 – 12000 = 360 R
=> 2160 = 360R
=> R = 2160/360 = 6%

9. Aman started a business by investing Rs 56000. After 5 months, Bharti joined him with a capital of Rs 48000. At the end of the year Bharti received Rs 3250 as share of profit. What is the total profit at the end of the year?
Rs. 9000
Rs. 7980
Rs. 8800
Rs. 9550
Rs. 9750
Option E
Ratio of Aman’s profit to Bharti’s profit
= 56 × 12 : 48 × 7
= 2 : 1
Now, let Aman’s share in profit be 2x and that of Bharti be x.
Given x = Rs 3250
Total Profit = 2x + x
= 3250 × 3 = Rs. 9750

10. A bag contains 4 white and 5 blue balls. Another bag contains 5 white and 7 blue balls. What is the probability of choosing two balls such that one is white and the other is blue?
51/100
53/108
52/103
50/107
51/100
Option B
Case 1: Ball from first bag is white, from another is blue.
So, probability = 4/9 * 7/12 = 28/108
Case 1: Ball from first bag is blue, from another is white.
So, probability = 5/9 * 5/12 = 25/108