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111
If a group of 35 men can complete the excavation of a trench in 16 days, how many days will it take for 28 men to complete the same task?
Correct Option
Option A
Explanation
This is a work-rate problem where the total work is constant. The total work is 35 men * 16 days = 560 man-days. Dividing this total work by 28 men gives 560 / 28 = 20 days required to complete the trench.
112
If six individuals working 8 hours daily earn a total of Rs. 720 per week, how much will 8 individuals earn per week if they work 6 hours daily?
Correct Option
Option A
Explanation
Earnings are proportional to the total man-hours worked. In the first scenario, total man-hours = 6 men * 8 hours = 48 units. In the second scenario, total man-hours = 8 men * 6 hours = 48 units. Since the total man-hours remain identical, the weekly earnings remain the same at Rs. 720.
113
If the total wages for 6 men working for 15 days amount to Rs. 700, what would be the total wages for 9 men working for 12 days?
Correct Option
Option C
Explanation
Wages are directly proportional to the product of the number of men and the number of days worked. The initial work units are 6 men multiplied by 15 days, totaling 90 units for Rs. 700. The new work units are 9 men multiplied by 12 days, totaling 108 units. Calculating the proportion, 700 multiplied by (108 divided by 90) equals Rs. 840.
114
A group of students planned to complete a construction project in 25 days. If 10 students were absent, the project took 35 days to complete. How many students were in the original group?
Correct Option
Option C
Explanation
Using the inverse relationship between the number of workers and the time taken (Work = Workers * Days), we set up the equation: x * 25 = (x - 10) * 35. Simplifying this, 25x = 35x - 350, which leads to 10x = 350, so x = 35.
115
What is the numerical probability value assigned to a sure or certain event?
Correct Option
Option D
Explanation
In probability theory, the likelihood of an event occurring is measured on a scale from 0 to 1. An impossible event has a probability of 0, while a sure or certain event, which is guaranteed to happen, is assigned a probability value of exactly 1.
116
What is the numerical probability value assigned to an impossible event?
Correct Option
Option A
Explanation
In probability theory, the likelihood of an event occurring ranges from 0 to 1. An impossible event is defined as an event that cannot occur under any circumstances, and therefore, it is assigned a probability value of exactly 0.
117
Which of the following values is impossible for the probability of an event?
Correct Option
Option B
Explanation
In probability theory, the likelihood of an event occurring is represented by a real number between 0 and 1, inclusive. A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event. Negative values are mathematically undefined in the context of standard probability, making them impossible outcomes for any event.
118
Determine the total number of possible outcomes when a standard six-sided die is rolled once.
Correct Option
Option A
Explanation
A standard fair die is a cube with six faces, each marked with a distinct integer from 1 to 6. When the die is rolled, any one of these six faces can land on top. Therefore, there are exactly 6 mutually exclusive and equally likely outcomes for a single roll of the die.
119
A box contains 8 red, 7 blue, and 6 green balls. If one ball is selected at random, what is the probability that the ball is neither red nor green?
Correct Option
Option A
Explanation
The total number of balls is 8 + 7 + 6 = 21. The condition 'neither red nor green' implies the ball must be blue. There are 7 blue balls. The probability is the number of favorable outcomes divided by the total outcomes, which is 7/21. Simplifying this fraction results in 1/3.
120
A bag contains 6 black balls and 8 white balls. If one ball is selected at random, what is the probability that the chosen ball is white?
Correct Option
Option C
Explanation
The total number of balls in the bag is 6 + 8 = 14. The number of favorable outcomes (selecting a white ball) is 8. The probability is calculated as the ratio of favorable outcomes to the total number of outcomes, which is 8/14. Simplifying this fraction by dividing both numerator and denominator by 2 gives 4/7.
