A basket contains 3 blue, 5 black and 3 red balls. If two balls are drawn at random, what is the probability that none of them is blue?
22/55
3/55
28/55
9/11
None of these
Answer: Option C.
Here n(S) = 11C2
Now, two balls can be drawn from 5(black)+3(red) balls = 8 balls in 8C2 ways
∴ n(E) = 8C2
Now, P(E) = 8C2/11C = 28/55
Other method:
Required probability
= 1 - (27/55) = 28/55
A basket contains 3 blue, 5 black and 3 red balls. If 2 balls are drawn at random, what is the probability that one is black and one is red?
2/11
8/11
9/11
3/11
None of these
Answer: Option D.
Selecting 1 black ball out of 5 = 5C1 ways
Selecting on red ball out of 3 = 3C1 ways
The required probability = (5C1 × 3C1)/11C2 = 3/11
What should come in place of question mark (?) in the following number/alphabetic series?
24 ? 109 134 150 159
71
65
86
53
None of these
Answer: Option E.
73
Here, 24+72=73
73+62=109
109+52=134
134+42=150
150+32=159
Hence, the question mark(?)should be replaced by 73.
A boat takes 8 hours to cover a distance while travelling upstream, whereas while travelling downstream it takes 6 hours. If the speed of the current is 4 kmph, what is the speed of the boat in still water?
12 kmph
28 kmph
16 kmph
Cannot be determined
None of these
Answer: Option B.
No matter if the boat goes upstream or downstream, Distance covered is same. So we can simply equate the two distances.
We have (x+4) × 6 = (x-4) × 8
Where x = speed of the boat in still water
Now, 6x + 24 = 8x - 32 or x = 28
Hence, the required speed = 28 km/hour
A man buys a land and gives for it 20 times the annual rent Find the rate of interest he gets for his money.
10%
24%
45%
18%
5%
Answer: Option E.
Let annual rent is 1 Rs. so buys the land at 20 Rs. So by investing Rs.20 he is getting Rs.1 as interest. so on Rs.100 he gets Rs.5 . so rate%=5%.Hence option E is the answer.
A man while returning from his factory, travels 2/3 of the distance by bus, 3/4 of the rest by car and remaining by foot. If he travels 2 km on foot, find the distance covered by him.
24km
22km
28km
26km
None of these
Answer: Option A.
Let total distance be D kms
2/3D + 1/3*3/4D + 2 = D
Therefore D = 24 km
Or going by options
Bus = (2/3) * 24 = 16,
Remaining = 24 - 16 = 8, car = (3/4) * 8 = 6
Total distance = 16 + 6+ 2 = 24km
Mira’s expenditure and saving are in the ratio 3:2. Her income increases by 10%. Her expenditure also increases by 12%. By how much % do her saving increase?
7%
9%
10%
13%
None of these
Answer: Option A.
Let total income be = 5
Increased income will be = 5.5
Increased expenditure will be = 3.36
Increased saving will be = 5.5 - 3.36 = 2.14
Percentage increase will be = (14/2) * 100 = 7%<
A thief goes away in a car at a speed of 60 kmph. A cop starts chasing the thief after 15 minutes in a car at a speed of 80 kmph. When will the cop overtake the thief from the start?
30 minutes
36 minutes
40 minutes
45 minutes
50 minutes
Answer: Option D
In 15 minutes thief will be 15 Km away . There will be a gap of 15 Km between thief and police . This gap will be covered with a relative speed of 80 -60=20 Km/h .So thief will be overtaken in 15/20 hours= 45 minutes.
A shopkeeper sells sugar at a profit of 20% and uses a weight which is 25 % less. What is total % gain?
45%
22.5%
55%
60%
None of these
Answer: Option D.
Let cost of 1 gram of sugar is 1 Rs.
So cost price of 1000 gram is 1000Rs.
As per question, Selling price of 1000 gram is 1200 Rs.
But he uses weight 25% less i.e. 750 gram for a Kg.
So SP of 750 gram is 1200 Rs. while its CP is 750 Rs.
Hence profit %=450/750 =3/5=60%
In an examination it is required to get 296 of the total maximum aggregate marks to pass. A student gets 259 marks and is declared failed. The difference of marks obtained by the student and that required to pass is 5%. What are the maximum aggregate marks a student can get?
690
780
740
749
None of these
Answer: Option C.
Let the aggregate marks be x
Therefore, 296 - 259 = 37 will be 5% of the x
Thus, (5/100) * x = 37
=> x = 740
