1. A bag contains 6 Black and 7 White balls. Four balls are drawn out one by one and not replaced. What is the probability that they are alternatively of different colours ?
A. 17/143
B. 21/143
C. 12/143
D. 11/143
E. None of these
Sol. Balls are picked in two manners – BWBW or WBWB
So probability = (6/13)*(7/12)*(5/11)*(6/10) + (7/13)*(6/12)*(6/11)*(5/10)
= 42/286 = 21/143.
2. A sum of Rs 4000 was lent partly at 5% and partly at 8% interest. Total interest received after 3 years was Rs 717. Find the ratio of the money lent at 5% and 8% ?
A. 16:29
B. 13:17
C. 27:13
D. 29:15
E. None of these
Sol. Suppose money lent at 5% = Rs x
Money lent at 8% = Rs (4000 – x)
Time (T) = 3 years
Interest in the first case = x*5*3/100 = 15x/100
Interest in the second case = Rs (4000 – x)*8*3/100
According to the question,
15x/100 + (3100 – x)*8*3/100 = 717
15x + 96000 – 24x = 71700
9x = 24300
x = Rs 2700
Other amount = Rs (4000 – 2700) = Rs 1300
Hence, ratio of money lent
= 2700: 1300 = 27:13.
3. A boat can travel 8.4km downstream in 14min. If the ratio of the speed of the boat in still water to the speed of the stream is 8:1. How much time will the boat take to cover 16.8km upstream ?
A. 26
B. 28
C. 38
D. 36
E. None of these
Sol. Speed = 8x:x
Downstream = 9x; upstream = 7x
Downstream speed = 8.4*60/14 = 36kmph
9x = 36
X = 4
Upstream = 7*4 = 28kmph
Time taken for 16.8km = 16.8*60/28 = 36min.
4. In a library 20% books are in Science, 50% of the remaining are in Social and the remaining 9000 are in various other subjects. What is the total number of books in Social ?
A. 6000
B. 9000
C. 4500
D. 2250
E. None of these
Sol. Let the no of books be x
Science books = 20% of x = 20/100 = x /5
Remaining = x – x /5 = 4x / 5
Social books = 50/ 100 x 4x / 5 = 2x/ 5
For other Subjects=> x – (x/5 + 2x/5) = 9000
2x / 5 = 9000
X = 22500
Social = 2*22500/5 = 9000.
5. Rahul and Murali buy two goods for Rs. 2000 and Rs. 3000 respectively. Rahul marks his goods up by x%, while Murali marks his goods up by 2x%. If the profit of Murali is Rs.12000 more than Rahul find x ?
A. 5%
B. 7%
C. 8%
D. 3%
E. None of these
Sol. SP of Rahul = 2000 + 2000*x = 2000 (1 + x)
Profit of Rahul = 2000 (1 + x) – 2000
SP of Murali = 3000 + 3000*2x = 3000 (1 + 2x)
Profit of Murali = 3000 (1 + 2x) – 3000
Diff of profit = 12000
[3000 (1 + 2x) – 3000] – [2000 (1 + x) – 2000] = 12000
4000x = 12000
X = 3.
Directions(6-10): What should come in place of (_) in the following series:
6. 11, 13, 20, 48, 111, _
A. 278
B. 268
C. 237
D. 256
E. 258
Sol. 11 + 1³ + 1 = 13
13 + 2³ – 1 = 20
20 + 3³ + 1 = 48
48 + 4³ – 1 = 111
7. 5, 7, 3, 11, -5, _
A. 25
B. 18
C. 30
D. 27
E. None of these
Sol. 5 + 2^1 = 7
7 - 2^2 = 3
3 + 2^3 = 11
11 - 2^4 = -5
-5 + 2^5 = 27
8. 61, 82, 124, 187, _, 376
A. 238
B. 248
C. 288
D. 271
E. None of these
Sol. 61 + (1 * 21) = 82
82 + (2 * 21) = 124
124 + (3 * 21) = 187
9. 23, 30, 46, 80, 141, _
A. 238
B. 248
C. 288
D. 271
E. None of these
Sol. 30 – 23 = 7
46 – 30 = 16
80 – 46 = 34
16 – 7 = 9
34 – 16 = 18….
10. 39, 52, 78, 117, 169, _
A. 246
B. 148
C. 188
D. 234
E. None of these
Sol. 13 * 3 = 39
13 * 4 = 52
13 * 6 = 78
13 * 9 = 117.
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