Comprehension And Aptitude Skills - Internals - Part - B

Explanation
If one third of a number is four times eleven, we can first find the value of the number. Four times eleven is equal to forty-four. So, one third of the number is forty-four. To find the whole number, we can multiply forty-four by three, which gives us one hundred and thirty-two. Finally, half of this number is sixty-six.

Explanation
At 6:30 am, the minute hand would be pointing at the 6 on the clock, while the hour hand would be pointing slightly past the 6. The angle between the two hands is calculated by taking the difference between the positions of the hour and minute hands. In this case, it would be 30 degrees (360 degrees divided by 12 hours, multiplied by 0.5 hours). Therefore, the correct answer is 30 degrees.

Explanation
The value of p+q+r can be calculated by substituting the respective values of p, q, and r from the given equation. Since p corresponds to the 16th letter of the alphabet, q corresponds to the 17th letter, and r corresponds to the 18th letter, the sum of their values would be 16 + 17 + 18 = 51.

Explanation
The shortest distance between A and E can be found by considering the given information. A is 8 miles east of B, C is 10 miles north of B, D is 13 miles east of C, and E is 2 miles north of D. By connecting these points, we can form a right-angled triangle with sides of 8 miles and 10 miles. Using the Pythagorean theorem, we can calculate the hypotenuse, which is the shortest distance between A and E. The calculation yields a distance of 13 miles.

Explanation
A two-digit number can have a maximum square value of 81 (9^2). However, the only two-digit numbers whose square ends with 8 are 18 and 78. Since there are no other two-digit numbers with a square ending in 8, the correct answer is 0.

Explanation
To find twenty percent of 25% of 20, we first calculate 25% of 20 which is 5. Then, we find twenty percent of 5 which is 1. Therefore, the answer is 1.

Explanation
The time taken for the train to cross the platform can be calculated by adding the time taken to cross the train's length and the time taken to cross the platform's length. The time taken to cross the train's length can be calculated using the formula: time = distance/speed. The distance is 150 meters and the speed is 45 kmph, which needs to be converted to m/s by dividing by 3.6. The time taken to cross the platform's length is 250 meters. Adding these two times together gives a total time of 32 seconds.

Explanation
The code for each letter in the word "RANGE" is determined by its position in the alphabet. The code for "R" is 1, "A" is 2, "N" is 3, "G" is 4, and "E" is 5. Similarly, in the word "RANDOM", the code for "R" is 1, "A" is 2, "N" is 3, "D" is 6, "O" is 7, and "M" is 8. Applying the same pattern, the code for "MANGO" would be 8 for "M", 2 for "A", 3 for "N", 4 for "G", and 3 for "O". Therefore, the correct answer is 82543.

Explanation
The value of p+q+r can be calculated by substituting the corresponding values for each letter. Since p = 16, q = 17, and r = 18, the sum of these values is 16+17+18 = 51.

Explanation
The shortest distance between A and E can be found by adding the distances of each segment of the path. A is 8 miles east of B, C is 10 miles north of B, D is 13 miles east of C, and E is 2 miles north of D. Therefore, the total distance is 8 + 10 + 13 + 2 = 33 miles. However, since we are looking for the shortest distance, we need to consider that A and E are in a straight line. Therefore, the shortest distance between A and E is the distance from A to D (8 + 10 + 13 = 31 miles) plus the distance from D to E (2 miles), which equals 33 miles.

Explanation
The square of a number with a units digit of 8 will always have a units digit of 4. Therefore, there are no two-digit numbers whose square ends with 8.

Explanation
To find twenty percent of 25% of 20, we first calculate 25% of 20 which is 5. Then, we find twenty percent of 5 which is 1. Therefore, the answer is 1.

Explanation
The length of the train is 150 meters and the length of the platform is 250 meters. The train is traveling at a speed of 45 kmph. To calculate the time it takes for the train to cross the platform, we need to consider the total distance that the train needs to cover, which is the sum of the length of the train and the length of the platform. Therefore, the total distance is 150 + 250 = 400 meters. Now, we can use the formula time = distance/speed to calculate the time it takes for the train to cross the platform. Plugging in the values, we get time = 400/45 = 8.89 seconds. However, we need to convert the time from seconds to seconds, so rounding off to the nearest second, the answer is 32 seconds.

Explanation
In the given code, each letter is assigned a unique number. By comparing the codes for "RANGE" and "RANDOM," we can see that the letters 'R,' 'A,' 'N,' and 'G' have the same code in both words, which is 1, 2, 3, and 4 respectively. Therefore, the code for the letter 'M' in "MANGO" would also be 1. The letters 'O' and 'D' have the code 3 and 5 respectively in "RANDOM," so the code for 'O' in "MANGO" would be 3 and the code for 'D' would be 5. Hence, the code for "MANGO" would be 82543.

Explanation
On 31st December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31st December 2009, it was Thursday.

Thus, on 1st Jan, 2010 it is Friday.

Explanation
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

5x = 20

x = 4.

Age of the youngest child = x = 4 years.

Explanation
Let the number of hens be x and the number of cows be y.

Then, x + y = 48 .... (i)

and 2x + 4y = 140 x + 2y = 70 .... (ii)

Solving (i) and (ii) we get: x = 26, y = 22.

The required answer = 26.

Explanation
Vikas spends 65% of his earnings, which is Rs. 720. To find his savings, we need to subtract the amount he spends from his earnings. 65% of Rs. 720 is Rs. 468, so his savings would be Rs. 720 - Rs. 468 = Rs. 252.

Explanation
When the bucket is half-filled with water, it weighs 30kg. This means that the weight of the water alone is 30kg. Therefore, the weight of the empty bucket is 30kg - 30kg = 0kg. Since the weight of the empty bucket is 0kg, the correct answer is 10kg.

Explanation
The clock loses 10 minutes each hour, so after 3 hours, it would have lost 30 minutes. Therefore, the clock would be 30 minutes behind the actual time. Since the clock was set correctly at noon, it would read 3 PM at 3:30 PM. However, since the clock is 30 minutes behind, the actual time would be 3:30 PM + 30 minutes, which is 3:36 PM.

Explanation
The speed of the train is given as 60 km/hr. To find the length of the train, we can use the formula: length = speed × time. The time taken to cross the pole is given as 9 seconds. Converting the speed from km/hr to m/s, we get 60 km/hr = 60 × (1000/3600) m/s = 50/3 m/s. Plugging in the values, we have length = (50/3) × 9 = 150 m. Therefore, the length of the train is 150 m.

Explanation
The length of the platform can be calculated by subtracting the distance covered by the train in 20 seconds (the time it takes to pass the man) from the total distance covered by the train in 36 seconds. The distance covered by the train in 20 seconds can be calculated using the formula Distance = Speed × Time. Converting the speed of the train from km/hr to m/s (by dividing by 3.6), we can calculate the distance covered in 20 seconds. Subtracting this distance from the total distance covered in 36 seconds gives us the length of the platform, which is 240 m.

Explanation
A alone can do 1/6th of the work in a day, while B alone can do 1/8th of the work in a day. Together, they can do 1/6 + 1/8 = 7/24th of the work in a day. Since they completed the work in 3 days, the total work is 3 * (7/24) = 7/8th. The remaining 1/8th of the work was done by C. Since they were paid Rs. 3200 for the entire work, the amount to be paid to C is (1/8) * 3200 = Rs. 400.

Explanation
The sum of two numbers is 22 and their difference is 4. To find the numbers, we can set up a system of equations. Let's call the two numbers x and y. The first equation is x + y = 22, and the second equation is x - y = 4. Solving this system of equations, we can add the two equations to eliminate y and find that 2x = 26, which means x = 13. Substituting x = 13 into one of the equations, we can find y = 9. Therefore, the numbers are 13 and 9.

Explanation
If 65% of the total examinees passed and the number of failures is 420, then the remaining 35% of the examinees failed. We can set up a proportion to find the total number of examinees. Let x be the total number of examinees. We can write the proportion as 35/100 = 420/x. Cross multiplying, we get 35x = 42000. Dividing both sides by 35, we find x = 1200. Therefore, the total number of examinees is 1200.