Twice the speed of a boat downstream is equal to thrice the speed upstream. The ratio of its speed in still water to the speed of current is
1 : 5
1 : 3
5 : 1
2 : 3
Answer : Option C.
Let the boat speed in still water be b.
Let the stream speed be x.
2(b+ x) = 3(b-x)
5x=b
b/x=5/1
A person has a chemical of Rs. 25 per litre. In what ratio should water be mixed with that chemical so that after selling the mixture at Rs. 20/litre he may get a profit of 25%?
13 : 16
12 : 15
9 : 16
19 : 22
Answer : Option C.
This can be solved using alligation.
What is required at the end of mixing is a price of 20/1.25 = 16.
So the alligation would look like this –
Water/0 Mixture/16 Chemical/25
Hence the ratio would be (25 – 16) : 16 = 9 : 16
Hence required ratio of Water : Chemical is 9:16.
The difference between the simple interest and compound interest on a certain sum of money for 2 years at 15% p. a. is Rs. 45. Find the sum.
Rs. 2700
Rs. 2500
Rs. 2000
None of these
Answer : Option C.
Since we know that the interest rate is 0.15, and knowing that the difference between two years of compound interest is nothing but interest on interest, we can find the first year’s interest as –
45/0.15 = 300.
Now if the interest is 300 at the end of one year, then the principal is 300 / 0.15 = 2,000
How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively, and the sum of terms is 40?
15
10
5
20
Answer : Option B.
Now the common difference of this AP is 16/4 = 4.
The sum of an AP is n/2 {2a + (n – 1)d}
Substituting we get, 40 = n/2 {2×-14 + (n – 1)4}
The best way to solve this is by plugging options. Put in n = 10 and get the RHS as 40.
In a class, 50 students play cricket, 20 students play football and 10 play both cricket and football. How many play at least one of these two games?
10
80
50
60
Answer : Option D.
The required answer is 50 + 20 – 10 = 60.
A bottle is full of Dettol. One-third of it is taken out and then an equal amount of water is poured into the bottle to fill it. This operation is done four times. Find the final ratio of dettol and water in the bottle.
13 : 55
20 : 74
16 : 65
10 : 48
Answer : Option C.
As in denominator we have to take 1/3 four times so, we start by assuming 81 ml of dettol in the bottle. After the first iteration you will be left with
2/3 × 81 = 54 ml. After the second iteration you will be left with
2/3 × 54 = 36 ml. After the third iteration you will be left with
2/3 × 36 = 24 ml. After the fourth iteration you will be left with
2/3 × 24 = 16 ml. So the required ratio will be 16 : (81 – 16) = 16 : 65
In a survey of defaulted payments of electrical bills of a residential complex of 125 houses, it is found that 50 houses defaulted on their payment of electrical bills in January, 60 in February and 40 in March. Houses can default in consecutive months only. 20 defaulted in January and February. 10 defaulted in February and March. How many houses defaulted in all the 3 months?
3
5
7
9
Answer : Option B.
We use formula for intersection of three sets, keeping in mind that Jan ∩ Mar does not exist, since they are not consecutive months.
Let x be the number of people defaulting in all 3 months.
We get the equation as : 125 = 50 + 60 + 40 – 20 – 10 + x. Solving we get x = 5.
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 metres away from the tree the angle of elevation becomes 30°. The breadth of the river is
40 m
20 m
30 m
60 m
Answer : Option B.
Let the breadth of the river be x, Using tangent rule we get,
So x = 20
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1, 2 are 0.45, 0.05 and 0.50 respectively. Assuming that outcomes are independent, the probability of India getting at least 7 points is
0.8750
0.0624
0.0875
0.0250
Answer : Option C.
Getting 7 points is possible in 2 cases.
Case 1: India wins all 4 matches.
Probability: (.5)4 = .0625.
Case 2: India wins any of the 3 matches and draws the remaining match. This can happen in total 4 ways. Probability: 4 x (.50)3 x (.05) = .025.
So, required probability: .0625 + .025 = .0875
Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it is
1/5
1/3
2/5
None of these
Answer : Option C.
Joint probability of all not being able to solve it is
2/3*3/4*4/5=2/5
