1.
If 2019 Christmas was on Friday, what day of the week will be 2021 Valentines day?
Correct Answer
B. Monday
Explanation
Christmas in 2019 was on a Friday. In a non-leap year, there are 365 days, which is equivalent to 52 weeks and 1 day. Since 2020 was a leap year, it had 366 days, which is equivalent to 52 weeks and 2 days. Therefore, 2021 will start on a Friday. Counting the days from January 1st to February 14th, which is Valentine's Day, there will be 45 days. Since 45 divided by 7 leaves a remainder of 3, it means that Valentine's Day in 2021 will be 3 days after Friday, which is Monday.
2.
Sankar secured 40% marks in an examination. He applied for revaluation and got his marks increased by 50%, he fails by 35 marks. If his post revaluation score is increased by 20% more, he will have 7 marks more than the passing score. What is the maximum mark of the examination.
Correct Answer
C. 350
3.
Arun and Bansan can together finish a work in 12 days. If Arun work half as efficient as he usually does and Bansan had worked thrice as efficient as he usually does, the work would have been completed in 9 days. How many days would Arun take to finish the work if he works alone at his usual efficiency?
Correct Answer
A. 18
Explanation
If Arun and Bansan can finish the work together in 12 days, it means that their combined efficiency is 1/12 of the work per day. Let's assume Arun's usual efficiency is x and Bansan's usual efficiency is y.
According to the given information, if Arun works half as efficient (x/2) and Bansan works thrice as efficient (3y), the work would be completed in 9 days.
So, their combined efficiency in this scenario is (x/2 + 3y) and it is equal to 1/9 of the work per day.
Now, we can set up an equation to find the values of x and y.
(x/2 + 3y) = 1/9
Simplifying the equation, we get x + 6y = 2/9
Since we know that their combined efficiency is 1/12, we can also set up another equation:
x + y = 1/12
Solving these two equations simultaneously will give us the values of x and y.
Once we know Arun's usual efficiency (x), we can find out how many days he would take to finish the work alone at his usual efficiency by setting up the equation:
x = 1/t (where t is the number of days)
Simplifying this equation will give us the value of t, which is the answer to the question.
4.
The average value of 80 numbers is 60 but it was found that three numbers 12, 15 and 17 are mistakenly calculate as 65, 70 and 79. Find the new average
Correct Answer
C. 78
Explanation
The new average can be found by subtracting the sum of the mistakenly calculated numbers (65+70+79) from the sum of the original 80 numbers and then dividing by 80. This gives us (60*80 - (65+70+79))/80 = 78.
5.
Covid 19 spread can be controlled with the use of sanitizers. Sanitizer is made up of Isopropyl alcohol and glycerine. How much glycerine costing Rs. 60 a litre should be mixed with 20 litres of isopropyl alcohol costing Rs. 120 a litre, so that the sanitiser can sold at Rs 110 a litre after taking a profit of Rs 10 per litre.
Correct Answer
C. 10
Explanation
To find the amount of glycerine needed, we can set up a proportion using the cost of the glycerine and the cost of the isopropyl alcohol. Let x be the amount of glycerine in litres. The cost of the glycerine is Rs. 60 per litre, so the cost of x litres of glycerine would be 60x. The cost of the isopropyl alcohol is Rs. 120 per litre, so the cost of 20 litres of isopropyl alcohol would be 120*20 = 2400. The total cost of the mixture is the sum of the cost of glycerine and the cost of isopropyl alcohol, which is 60x + 2400. The selling price is Rs. 110 per litre, and the profit is Rs. 10 per litre, so the selling price of the mixture is 110*(x+20). Setting up the proportion, we get (60x + 2400)/(x+20) = 110. Solving for x, we find x = 10. Therefore, 10 litres of glycerine should be mixed with 20 litres of isopropyl alcohol.
6.
In the given figure, ABCD is a rectangle and ABE is an equilateral triangle with common side AB of length 12cm and E is the midpoint of CD. Five parallel lines cut the rectangle ABCD into equal areas. Find the area of the shaded region.
Correct Answer
A.
7.
Find the highest power of 21 in 100!
Correct Answer
C. 16
Explanation
To find the highest power of 21 in 100!, we need to determine the number of times 21 can be divided into 100!. Since 21 = 3 * 7, we need to count the number of times both 3 and 7 appear as factors in the prime factorization of numbers from 1 to 100. We know that the power of 3 in 100! is greater than the power of 7, so we only need to consider the power of 7. We can calculate the power of 7 in 100! by dividing 100 by 7, which gives us 14. Therefore, the highest power of 21 in 100! is 14.
8.
Netravati express, running at a speed of 54km/hr crosses Ernakulam town railway station Platform number one in 5 seconds. If the length of the train is 60m, what is the length of the platform?
Correct Answer
B. 90m
Explanation
The train is crossing the platform, so the total distance covered by the train and the platform is equal to the length of the train. The train is 60m long and it takes 5 seconds to cross the platform. Therefore, the speed of the train is 60m/5s = 12m/s. We can convert the speed from m/s to km/hr by multiplying it by 3.6. So, the speed of the train is 12m/s * 3.6 = 43.2 km/hr. Since the train is running at a speed of 54 km/hr, the length of the platform can be calculated using the formula: length of platform = (speed of train * time taken to cross the platform) - length of train. Plugging in the values, we get: length of platform = (54 km/hr * 5s) - 60m = 270m - 60m = 210m. Therefore, the length of the platform is 210m, which is not one of the given options. Hence, the given answer of 90m is incorrect.
9.
A car was travelling a distance of 140km from Kochi to Calicut. After covering 60km, the car develops an engine trouble and travelled the rest of the journey at two-third of its original speed. It arrived Calicut two hours late than the normal time. What is the normal speed of the car is?
Correct Answer
C. 30
Explanation
The car travelled 140 - 60 = 80km at two-thirds of its original speed.
Let the normal speed of the car be x km/h.
The time taken to cover the first 60km is 60 / x hours.
The time taken to cover the remaining 80km is 80 / (2/3)x = 120 / x hours.
The total time taken for the journey is 60 / x + 120 / x = 180 / x hours.
It arrived 2 hours late, so the total time taken is the normal time + 2 hours.
Therefore, 180 / x = (140 / x) + 2.
Simplifying the equation, we get 180 = 140 + 2x.
Solving for x, we find x = 20.
Hence, the normal speed of the car is 20 km/h.
10.
The Head post office of Mirzpur has 10 consecutive pincodes under it. The post master, while sorting the letters spilled some water on a letter and the pincode got washed off. What is the pincode, if he remembers that the pincode is a perfect square.
Correct Answer
C. 231361
11.
The speed of a boat in still water is 18 km/hr and the rate of current is 7 km/hr. The distance travelled downstream in 36 minutes is:
Correct Answer
A. 15 km
Explanation
The speed of the boat in still water is given as 18 km/hr, and the rate of the current is 7 km/hr. To find the distance travelled downstream in 36 minutes, we need to convert the time to hours by dividing it by 60 (36/60 = 0.6 hours). The speed of the boat relative to the current is the sum of the speed in still water and the rate of the current (18 + 7 = 25 km/hr). Finally, we can calculate the distance travelled by multiplying the speed relative to the current by the time (25 * 0.6 = 15 km). Therefore, the correct answer is 15 km.
12.
Two pipes alpha and beta can fill a tank in 5 hours and 10 hours respectively. A hole on the bottom of the tank can drain the tank in 20 hours. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
Correct Answer
B. 4 hours
Explanation
The filling rate of pipe alpha is 1/5 of the tank per hour, and the filling rate of pipe beta is 1/10 of the tank per hour. The draining rate of the hole is 1/20 of the tank per hour. When both pipes are opened simultaneously, the combined filling rate is (1/5 + 1/10) = 3/10 of the tank per hour. The draining rate is 1/20 of the tank per hour. Therefore, the net filling rate is (3/10 - 1/20) = 5/20 = 1/4 of the tank per hour. It will take 4 hours to fill the tank at this rate.
13.
The difference between a number and its three-seventh is 36. Find then number formed by reversing the digits of the number.
Correct Answer
D. 36
Explanation
Let's assume the number is "x". According to the given information, the difference between "x" and its three-seventh is 36. So, we can write the equation as x - (3/7)x = 36. Simplifying this equation, we get (4/7)x = 36. Multiplying both sides by 7/4, we find x = 63. Reversing the digits of 63 gives us the number 36.
14.
Saran and John started from Kochi at 8:00 am and 9:00am respectively and reached Trivandrum on the same day at the same point of time. They reach their common destination at the same point of time. If Saran drove for at least 6 hours, then what will be the highest possible value of the percentage by which the speed of John could exceed that of Saran ?
Correct Answer
C. 20
Explanation
If Saran drove for at least 6 hours and both Saran and John reached their common destination at the same point of time, it means that John had less time to cover the same distance. Therefore, in order for John's speed to exceed Saran's by the highest percentage, John would need to cover the distance in the shortest amount of time possible. This would result in John driving for only 1 hour. Therefore, the highest possible value of the percentage by which John's speed could exceed Saran's is 20%.
15.
A’s salary is 20 % more than that of B and 20% less than that of C. If C’s salary is decreased by 4% and B’s salary is increased by 10%, then the percentage by which, C’s salary would exceed B’s salary is nearest to?
Correct Answer
D. 31 %