# Quant Test for NIACL AO Prelims Exam Set – 10

1. A boat can cover 21 km upstream and 60 km downstream in 9 hours. The speed of the boat in still water is 4 km/hr more than the speed of the stream. Find the time taken by the boat to cover 55 km upstream and 140 km downstream.
18 hours 10 minutes
20 hours 40 minutes
15 hours 20 minutes
28 hours 20 minutes
22 hours 30 minutes
Option E
Let the speed of the stream be x km/hr.
Speed of the boat in still water = x + 4 km/hr.
21/(x+4-x)+60/(x+4+x) = 9
=> x = 6
Upstream speed = 4 km/hr.
Downstream speed = 16 km/hr.
Required time = 55/4 + 140/16 = 22
hours 30 minutes

2. Area of the circular field is equal to the area of the rectangular field. Length of the rectangular field is 9 m more than the breadth of the rectangular field. Find the perimeter of the rectangular field, if the circumference of the circular field is 132 m.
95 m
110 m
80 m
150 m
100 m
Option D
Let the length of the rectangular field be x m.
Breath = (x-9) m
Radius = 132/2*pi = 21 m
Area of the circular filed = 22/7*21*21 = 1386 m^2
Area of the rectangular field = x(x-9) = 1386
=> x^2 – 9x – 1386 = 0
=> x^2 – 42x + 33x – 1386 = 0
=> x = 42, – 33
Perimeter = 2*(42+33) = 150 m

3. Puja invested Rs.10,000 in a scheme offering 20% compound interest compounded annually for three years. Rohit invested Rs.12000 in another scheme offering 25% compound interest for2 years. Find the difference between the interests earned by Puja and Rohit.
Rs.530
Rs.480
Rs.510
Rs.500
Rs.400
Option A
Interest earned by Puja = 10000*{(1+0.20)^3 – 1} = Rs.7280
Interest earned by Rohit = 12000*{(1+0.25)^2 – 1} = Rs.6750
Required difference = 7280 – 6750 = Rs.530

4. Puja invested Rs.10,000 in a scheme offering 20% compound interest compounded annually for three years. Rohit invested Rs.12000 in another scheme offering 25% compound interest for2 years. Find the difference between the interests earned by Puja and Rohit.

40
Either 15 or 35
35
50
15
Option B
Interest earned by Puja = 10000*{(1+0.20)^3 – 1} = Rs.7280
Interest earned by Rohit = 12000*{(1+0.25)^2 – 1} = Rs.6750
Required difference = 7280 – 6750 = Rs.530

5. A bag contains 50 bulbs, out of which certain number of bulbs are defective. Two bulbs are randomly drawn from the bag and the probability that a defective bulb and non-defective bulb are drawn is 3/7. Find the number of defective bulbs in the bag.
40
Either 15 or 35
35
50
15
Option B
Let the number of defective bulbs be x.
And the number of non-defective bulbs = (50-x)
Probability that a defective and a non-defective bulb are drawn = (xC1*(50-x)C1)/50C2 = 3/7 x^2 – 50x + 525 = 0
=> x^2 -35x – 15x + 525 = 0
=> x = 35,15
Either 15 or 35

6. How many four-letters words having at-least one vowel can be formed by using the letters of the word ‘BAKESHOP’?
1250
1320
1560
1660
1490
Option C
Total number of ways in which letters are selected
= 3C1*5C3 + 3C2*5C2 + 3C3*5C1 = 30+30+5 = 65
Four letters are arranged within the word = 4! = 24 ways
Total number of words formed = 24*65 = 1560

7. Directions(6-10):
Find out the odd one out from the following series.

8. 17,36,91,188,321,492
17
36
91
492
321
Option C
+19*1
+19*3
+19*5
+19*7
+19*9
93 should be in place of 91.

9. 21,27,52,116,197,231
52
21
27
116
231
Option E
+6^1
+5^2
+4^3
+3^4
+2^5
229 should be in place of 231.

10. 9,11,15,24,54,177
54
177
9
11
24
Option A
+1!+1
+2!+2
+3!+3
+4!+4
+5!+5
52 should be in place of 54.

11. 15,14,24,63,236,1175
14
24
15
1175
63
Option D
*1-1^2
*2-2^2
*3-3^2
*4-4^2
*5-5^2
1155 should be in place of 1175.