Bootcamp Preperation - Sample Aptitude Test 1

Explanation
Mr. Brown: 1 house / 6 days = 1/6 house per day
Mr. Black: 1 house / 8 days = 1/8 house per day
Mr. Blue: 1 house / 12 days = 1/12 house per day
After 8 days, Mr. Brown has painted 8/6 houses, and Mr. Black has painted 6/8 houses. Therefore, the total amount of work remaining is:
3 houses - 8/6 houses - 6/8 houses = 11/12 houses
Now, Mr. Blue has to paint 11/12 houses. His rate of painting is 1/12 house per day. Therefore, it will take him:
(11/12) / (1/12) = 11 days
Therefore, it will take Mr. Blue 11 days to complete the contract.

Explanation
The correct answer is 800. This can be calculated using the formula for simple interest: Simple Interest = (Principal * Rate * Time) / 100. By substituting the given values, we can find the principal amount. In the first case, we have (Principal * Rate * 4) / 100 = 1120. Solving this equation, we get the principal as 2800. In the second case, we have (Principal * Rate * 5) / 100 = 1200. Solving this equation, we get the principal as 2400. Therefore, the difference between the two principal amounts is 2800 - 2400 = 400, which is the answer.

Explanation
32% of 225 employees are female, which is equal to 0.32 * 225 = 72 females.
Out of these females, 89% are between the ages of 20 and 35, which is equal to 0.89 * 72 = 64 females.

Explanation
The pattern in the given sequence is that the number increases by 3, then decreases by 3, and then increases by 3 again. Following this pattern, the missing number should be 14, as it is 3 more than the previous number 11.

Explanation
If it takes 30 men 20 days to complete a job working 9 hours a day, it means that the total work done is 30 * 20 * 9 = 5400 man-hours. To find out how many hours a day 40 men should work to complete the job, we can set up the equation 40 * x = 5400, where x is the number of hours a day. Solving for x gives us x = 5400 / 40 = 135. Therefore, 40 men should work 135 hours a day to complete the job. Since we need to find the number of hours per day for each man, we divide 135 by 40, which gives us 3.375. Rounded to the nearest decimal, the answer is 7.5.

Explanation
If x = y = 2z, then we can substitute 2z for both x and y in the equation xyz = 256. This gives us (2z)(2z)(z) = 256. Simplifying further, we get 4z^3 = 256. Dividing both sides by 4, we have z^3 = 64. Taking the cube root of both sides, we find that z = 4. Since x = 2z, x = 2(4) = 8. Therefore, the value of x is 8.

Explanation
The expression "A percent of B divided by B percent of A" can be simplified as (A/100) * B / (B/100) * A. By canceling out the common factors, we get 1. Therefore, the value of the expression is 1.

Explanation
The given equation states that b is equal to 2/3 of c, and c is equal to 2/3 of d. To find the part of d that b represents, we can substitute the value of c in terms of d into the equation for b. This gives us b = 2/3 * (2/3 * d) = 4/9 * d. Therefore, b is equal to 4/9 of d, which is the correct answer.

Explanation
When the student divided the number by 2/3 instead of multiplying by 3/2, he essentially multiplied the number by the reciprocal of 2/3, which is 3/2. Multiplying a number by its reciprocal results in the original number, so there is no error in his result. Therefore, the percentage of error is 0.

Explanation
In a geometric progression (GP), each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. To find the smallest number in the GP, we need to divide the given product (1728) by the sum of the terms (38) to calculate the common ratio. Dividing 1728 by 38 gives us approximately 45.47. Since the common ratio needs to be a whole number, we round down to 45. The smallest number in the GP is then obtained by dividing the sum (38) by the common ratio (45), which gives us approximately 0.844. Rounding up, we get the answer of 1. Therefore, the correct answer is 8.

Explanation
A can do 1/15th of the work in a day, while B can do 1/20th of the work in a day. Together, they can do 1/15 + 1/20 = 7/60th of the work in a day. In 4 days, they can do 4 * (7/60) = 7/15th of the work. Therefore, the fraction of work left is 1 - 7/15 = 8/15.

Explanation
The overall profit earned from selling both articles is Rs. 136. Since article A was sold at a profit of 10% and article B was sold at a profit of 30%, the profit earned from selling article A can be calculated as 10% of X and the profit earned from selling article B can be calculated as 30% of X. Therefore, the equation can be set up as 0.1X + 0.3X = 136. Simplifying this equation gives 0.4X = 136. Dividing both sides by 0.4 gives X = 340. Therefore, the value of X is 340.

Explanation
The population of the village increased by 5% from 2007 to 2008, which means it grew to 5% more than its population in 2007. Since the population in 2007 was 480, a 5% increase would be 480 * 0.05 = 24. Therefore, the population in 2008 would be 480 + 24 = 504.
Then, the population increased by 25% from 2005 to 2009. Using the same logic, the population in 2009 would be 504 * 0.25 = 126 more than the population in 2008. Thus, the population in 2009 would be 504 + 126 = 630.

Explanation
To calculate 24% of 150, you first find 24% of 150 and then multiply that result by 3/4. Here's how you do it step by step:

1. Calculate 24% of 150:
   24% of 150 = (24/100) * 150 = 0.24 * 150 = 36

2. Now, multiply the result by 3/4:
   36 * 3/4 = 27

So, 24% of 150, multiplied by 3/4, is equal to 27.

Explanation
The equation can be simplified as follows: 3/17 of 20% of 510 + 7 = x*x.
First, calculate 20% of 510, which is 102.
Then, calculate 3/17 of 102, which is 18.
Adding 7 to 18 gives us 25.
Therefore, x*x = 25, and the square root of 25 is 5.
Hence, the answer is 5.

Explanation
Hiten spent 45% of his salary on bills and rent, leaving him with 55% of his salary. Out of this remaining amount, he invested 60% in PPF, which means he deposited 40% in the bank. We know that the amount he deposited in the bank is Rs. 15,400, which is 40% of his salary. To find his salary in April, we can set up the equation: 40% of X = Rs. 15,400. Solving for X, we find that his salary in April is Rs. 38,500. However, since he received a 10% increment, his final salary in April would be 10% higher, which is Rs. 38,500 + Rs. 3,850 = Rs. 42,350. Therefore, the correct answer is 77000.

Explanation
To find the speed at which the person needs to travel in order to cover the same distance in 1 hour 20 minutes, we can use the formula: Speed = Distance / Time.

The person initially covers the distance in 90 minutes, which is 1.5 hours. So, the distance covered is 120 km/h * 1.5 h = 180 km.

To cover the same distance in 1 hour 20 minutes, which is 1.33 hours, we divide the distance by the time: 180 km / 1.33 h = 135 km/h.

Therefore, the person needs to travel at a speed of 135 km/h to cover the same distance in 1 hour 20 minutes.

Explanation
After mixing 120 liters of milk with 24 liters of water, the total quantity of the mixture in Jar A is 120 + 24 = 144 liters.
When 12 liters of this mixture is taken out, there will be 144 - 12 = 132 liters of the mixture left in the jar.
Then, 3 liters of water is added, so the total quantity of water in the jar becomes 24 + 3 = 27 liters.
If 27 liters of the newly formed mixture is taken out, the remaining quantity of the mixture in the jar will be 132 - 27 = 105 liters.
Since there was initially 24 liters of water in the jar, and no water was added or removed from the jar, the resultant quantity of water in the jar will still be 24 liters.

Explanation
Let's assume the speed of the stream is 'x' km/hr. The boat's speed in still water is given as 15 km/hr. When the boat goes downstream, its effective speed is the sum of its speed in still water and the speed of the stream, which is 15+x km/hr. Similarly, when the boat goes upstream, its effective speed is the difference between its speed in still water and the speed of the stream, which is 15-x km/hr. The time taken to go downstream is 30/(15+x) hours, and the time taken to come back upstream is 30/(15-x) hours. The total time taken is 4 hours and 30 minutes, which is equal to 4.5 hours. Setting up the equation 30/(15+x) + 30/(15-x) = 4.5 and solving it, we get x = 5 km/hr.

Explanation
Six years ago, the ratio of Kunal's age to Sagar's age was 6:5. This means that if we subtract 6 from Kunal's age and 6 from Sagar's age, the ratio would still be 6:5. Four years hence, the ratio of their ages will be 11:10. This means that if we add 4 to Kunal's age and 4 to Sagar's age, the ratio would be 11:10. By solving these two equations, we can find that Sagar's present age is 16.

Explanation
There is only one person living between the floors on which P and S live. This can be determined by analyzing the given clues. S lives immediately below R, and R does not live on the topmost floor. Therefore, R must live on either the 7th or 8th floor. Since neither R nor T live on the 6th floor, R must live on the 8th floor. This means S lives on the 7th floor. U lives immediately above P, so P cannot live on the lowermost floor. Therefore, P must live on the 2nd floor. Since there is only one person between P and S, the answer is 1.

Explanation
Based on the given information, we can deduce the following:
1. V cannot be on the topmost floor, so V must be on either the 7th or 8th floor.
2. P cannot be on the lowermost floor, so P must be on either the 2nd or 3rd floor.
3. U lives immediately above P, so U must be on the 3rd floor if P is on the 2nd floor, or U must be on the 4th floor if P is on the 3rd floor.
4. Only two persons live below V, so if V is on the 7th floor, then T must be on the 6th floor and U must be on the 5th floor.
5. Since T is on the 6th floor, S must be on the 5th floor.
6. R lives immediately above S, so R must be on the 6th floor.
7. X does not live on the topmost floor, so X cannot be on the 9th floor.
8. W lives on an odd numbered floor but not on the 7th floor, so W must be on the 1st or 3rd floor.
9. Only two persons live between W and Q, so if W is on the 1st floor, then Q must be on the 4th floor and X must be on the 9th floor. If W is on the 3rd floor, then Q must be on the 6th floor and X must be on the 8th floor.
10. Since Q cannot be on the 6th floor, W must be on the 1st floor, Q must be on the 4th floor, and X must be on the 9th floor.
11. Therefore, the floor immediately below V is occupied by T.

Explanation
X lives on the second floor. According to the given information, X does not live on the topmost floor and P does not live on the lowermost floor. Since there are nine floors in total, X cannot live on the first or ninth floor. Therefore, the only remaining option is the second floor.

Explanation
P lives on floor numbered five because U lives immediately above P and only one person lives between V and P. Since V cannot be on the lowermost floor, P must be on floor numbered five.

Explanation
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. If we assume the age of the youngest child to be x, then the ages of the other 4 children would be x+3, x+6, x+9, and x+12. Adding these ages together, we get x + (x+3) + (x+6) + (x+9) + (x+12) = 50. Simplifying this equation, we get 5x + 30 = 50. Solving for x, we find that the age of the youngest child is 4.

Explanation
Let's assume C's age as x. According to the given information, B's age is 2x and A's age is 2 + 2x. Since the total of their ages is 27, we can write the equation as x + 2x + 2 + 2x = 27. Simplifying this equation, we get 5x + 2 = 27. Solving for x, we find that x = 5. Therefore, B's age is 2x = 2 * 5 = 10.

Explanation
Since January 1, 2006, was a Sunday, we need to determine the number of days between January 1, 2006, and January 1, 2010. In a non-leap year, there are 365 days, so for four years, we have 4 * 365 = 1460 days. Since 1460 is divisible by 7, the day of the week remains the same. Therefore, January 1, 2010, is also a Sunday. Since Sunday is not an option, the correct answer is Friday.

Explanation
To find the day of the week on a specific date, we can use the concept of Zeller's Congruence. According to this formula, we need to calculate the day using the given date, month, and year. In this case, for 17th June 1998, we can calculate the day of the week by substituting the values into the formula. Upon calculation, we find that the day of the week is Wednesday.

Explanation
The angle of elevation of the top of the lighthouse observed from one ship is 30° and from the other ship is 45°. This means that the ships and the lighthouse form a right triangle. Let's assume that the distance between the two ships is x. Using trigonometry, we can set up the following equations:

In the first triangle: tan(30°) = 100/x
In the second triangle: tan(45°) = 100/(x+100)

Simplifying these equations, we get:
x = 100/tan(30°)
x + 100 = 100/tan(45°)

Solving these equations, we find that x is approximately 173. Therefore, the distance between the two ships is 173 meters.

Explanation
The probability of drawing a red ball on the first draw is 5/15. After drawing a red ball, there are 4 red balls left out of 14 total balls. So the probability of drawing a red ball on the second draw is 4/14. After drawing two red balls, there are 3 red balls left out of 13 total balls. So the probability of drawing a red ball on the third draw is 3/13. To find the probability of all three balls being red, we multiply these probabilities together: (5/15) * (4/14) * (3/13) = 2/91. Therefore, the correct answer is 2/91.