1.
An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30º. The heights of the tower is:
Correct Answer
A. 21.6 m
Explanation
The observer's height and the distance from the tower form a right triangle. The angle of elevation is the angle between the observer's line of sight and the horizontal. In this case, the angle of elevation is 30Â°. Using trigonometry, we can use the tangent function to find the height of the tower. The tangent of 30Â° is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the tower). By rearranging the formula, we can find that the height of the tower is equal to the tangent of 30Â° multiplied by the distance from the tower. Substituting the given values, we find that the height of the tower is 21.6 m.
2.
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
Correct Answer
B. 40
Explanation
The given information states that 4 men and 6 women can complete the work in 8 days, while 3 men and 7 women can complete it in 10 days. This means that the work done by 1 man in 1 day is equal to the work done by 1 woman in 1 day. To find out how many days 10 women will take to complete the work, we can assume that 1 woman can complete the work in W days. Using the given information, we can set up the following equation: (4 men + 6 women) x 8 = (3 men + 7 women) x 10. Solving this equation, we find that W = 40. Therefore, 10 women will complete the work in 40 days.
3.
In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
Correct Answer
B. 25 m
Explanation
In the given question, it is stated that A can beat B by 31 m and C by 18 m in a race of 200 m. This means that A is faster than both B and C. Now, we need to find out by how much C will beat B in a race of 350 m. Since A is faster than both B and C, it can be inferred that C will beat B by a greater margin in a longer race. Therefore, the correct answer is 25 m.
4.
What will be the day of the week 15^{th} August, 2010?
Correct Answer
A. SUNDAY
Explanation
15th August, 2010 fell on a Sunday.
5.
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Correct Answer
B. 13
Explanation
The number of persons working on the road is inversely proportional to the number of days required to complete the work. Therefore, if the number of persons decreases from 39 to 30, the number of days required will increase. Additionally, if the number of hours worked per day increases from 5 to 6, the number of days required will decrease. Thus, it can be inferred that 30 persons, working 6 hours a day, will complete the work in 13 days.
6.
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
Correct Answer
C. 23 : 33 : 60
Explanation
The new salaries after the increments will be 115% of A, 110% of B, and 120% of C. Simplifying these percentages, we get 1.15A, 1.1B, and 1.2C. To find the new ratio, we divide each salary by the smallest one, which is A. This gives us 1.15A/A, 1.1B/A, and 1.2C/A. Simplifying further, we get 1.15, 1.1B/A, and 1.2C/A. Since we don't have the values of A, B, and C, we can't simplify any further. Therefore, the new ratio of their salaries is 23 : 33 : 60.
7.
Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Correct Answer
D. Rs. 10,500
Explanation
Simran and Nanda invested in the business for different durations. Simran invested for 3 years, while Nanda invested for 2.5 years (6 months is half a year). To calculate their share of the profit, we need to consider the ratio of their investments and the duration of their investments. The ratio of their investments is 50,000:80,000 or 5:8. Simran's share of the profit can be calculated as (5/13) * 24,500 = Rs. 9,423. Therefore, the correct answer is Rs. 9,423.
8.
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
Correct Answer
A. 400 m
Explanation
The train is crossing another train traveling in the opposite direction, so the relative speed between the two trains is the sum of their speeds, which is (48 + 42) kmph = 90 kmph. The train takes 12 seconds to completely cross the other train, so the length of the train is (90 kmph * 12 seconds) / (60*60) = 30 meters. The train also passes a railway platform in 45 seconds, so the total distance covered is the sum of the length of the train and the length of the platform. Therefore, the length of the platform is (45 seconds * 90 kmph) / (60*60) - 30 meters = 400 meters.
9.
David gets on the elevator at the 11^{th} floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
Correct Answer
C. 30
10.
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Correct Answer
C. 2/7
Explanation
The probability of getting a prize can be calculated by dividing the number of favorable outcomes (prizes) by the total number of possible outcomes (prizes + blanks). In this case, there are 10 prizes and 25 blanks, so the total number of possible outcomes is 10 + 25 = 35. Therefore, the probability of getting a prize is 10/35, which simplifies to 2/7.