1.
In an examination, P got 12% more marks than Q but 12.5% fewer marks than R. If the difference between the marks scored by Q and R is 350 then what is the score of P?
Correct Answer
D. 1400
Explanation
P got 12% more marks than Q, which means P's score is 112% of Q's score. P also got 12.5% fewer marks than R, which means P's score is 87.5% of R's score. The difference between Q and R's score is 350. Let's assume Q's score is x, then R's score is x + 350. Therefore, P's score is 0.875(x + 350). We need to find P's score, so we substitute the value of x as P's score and solve the equation: 0.875(P + 350) = P. Solving this equation, we get P = 1400. Therefore, the score of P is 1400.
2.
Pawan scored 33% marks in a subject and failed by 21 marks. If he scored 55% marks he would have got 45 marks more than pass marks. Find the maximum marks in the subject.
Correct Answer
A. 300
Explanation
Pawan scored 33% marks in the subject and failed by 21 marks. This means that he scored 33% of the maximum marks minus 21 marks. If he scored 55% marks, he would have got 45 marks more than the pass marks. This means that he scored 55% of the maximum marks minus the pass marks, which is equal to 45 marks. By solving these two equations, we can find that the pass marks is 150 and the maximum marks in the subject is 300.
3.
There are four boxes. The weight of the second box is 25% less than that of the first box whose weight is 600 kg. The weight of the third box is 27 7/9 % less than that of the second box, whose weight is 250 kg more than that of the fourth box. What is the total weight of the third and the fourth boxes?
Correct Answer
C. 525
Explanation
The weight of the first box is given as 600 kg. The weight of the second box is 25% less than the first box, which means it is 75% of the weight of the first box. Therefore, the weight of the second box is 600 kg * 75% = 450 kg. The weight of the second box is also given as 250 kg more than the weight of the fourth box. So, the weight of the fourth box is 450 kg - 250 kg = 200 kg. The weight of the third box is 27 7/9 % less than the weight of the second box, which means it is 100% - 27 7/9% = 72 2/9% of the weight of the second box. Therefore, the weight of the third box is 450 kg * 72 2/9% = 324 kg. The total weight of the third and fourth boxes is 324 kg + 200 kg = 524 kg.
4.
In a village, 39% of the residents are men and 32% of the residents are women and the remaining are children. The literate percentage among the children is 89%. The number of illiterate children in the village is 11,165. Find the number of females in the village.
Correct Answer
B. 112000
Explanation
The total population of the village can be calculated by dividing the number of illiterate children by the literacy rate among children, which is 89%. So, the total population of the village is 11,165 / 0.89 = 12,555.
From the given information, we know that 39% of the residents are men and 32% are women. So, the remaining percentage of residents are children, which is 100% - 39% - 32% = 29%.
To find the number of females in the village, we can multiply the total population by the percentage of women: 12,555 * 0.32 = 4,018.4.
Since the number of residents must be a whole number, we round this value to the nearest whole number, which is 4,018.
Therefore, the number of females in the village is 4,018.
Note: The given answer of 112,000 is incorrect.
5.
The base of the triangle is increased by 50%. Find the percentage increase in the area if the perpendicular height of the triangle is decreased by 20%.
Correct Answer
B. 20%
Explanation
When the base of a triangle is increased by 50%, the new base becomes 1.5 times the original base. When the perpendicular height of the triangle is decreased by 20%, the new height becomes 0.8 times the original height. The area of a triangle is calculated by multiplying the base by the height and dividing by 2. Therefore, the new area can be calculated by multiplying the new base by the new height and dividing by 2. Substituting the values, the new area is 1.5 * 0.8 = 1.2 times the original area. This represents a 20% increase in the area.
6.
Fresh grapes contain 80% water by weight and when the grapes are dried, raisins contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kg of raisins.
Correct Answer
C. 75
Explanation
To find out how many kilograms of fresh grapes are needed to get 20kg of raisins, we can use the concept of the water content in both fresh grapes and raisins. Since raisins contain 25% water by weight, it means that 75% of the weight is the actual fruit. Similarly, fresh grapes contain 80% water by weight, which means that 20% of the weight is the actual fruit. Therefore, to get 20kg of raisins, we need to have 20kg / 0.75 = 26.67kg of the actual fruit. Since the weight of the actual fruit is 20% of the weight of fresh grapes, we can calculate that 26.67kg is 20% of 133.33kg. Therefore, we need approximately 133.33kg of fresh grapes to get 20kg of raisins.
7.
In an election contested by 2 candidates A and B, A got 28% more votes than the B. If B got 175 votes, how many votes did A get. Assume that there were no invalid votes.
Correct Answer
A. 224
Explanation
Candidate A received 28% more votes than candidate B. If B received 175 votes, we can find A's votes by adding 28% of B's votes to B's votes. 28% of 175 is 49, so A received 175 + 49 = 224 votes.
8.
In an election contested by 2 candidates A and B, A got 28% of the total votes more than B. If B got 225 votes, then how many votes did A and B get? Assume that there were no invaid votes.
Correct Answer
A. 625
Explanation
Candidate B received 225 votes, which is 100% - 28% = 72% of the total votes. Therefore, 1% of the total votes is equal to 225/72 = 3.125 votes. Multiplying this by 100 gives us the total number of votes, which is 312.5. Since the number of votes cannot be a decimal, we round it up to the nearest whole number, which is 313. Therefore, Candidate A received 313 + 28% = 313 + 87.64 = 400 votes. The total number of votes that A and B received is 400 + 225 = 625 votes.
9.
A=B * C
Let A = Constant
If B increases by 20%, then C decreases by ___%.
Correct Answer
C. 16.66%
Explanation
If A is a constant and A = B * C, then any change in B or C will result in a change in A. In this case, if B increases by 20%, it means that B becomes 1.2 times its original value. To maintain A as a constant, C needs to decrease by a certain percentage. To find this percentage, we can set up the equation A = B * C and substitute the new values. We have A = (1.2B) * (C - x), where x is the percentage decrease in C. Simplifying this equation, we get A = 1.2BC - 1.2Bx. Since A is a constant, 1.2BC - 1.2Bx must be equal to the original value of A. Therefore, 1.2BC - 1.2Bx = BC. Solving for x, we find x = 0.1666, which is equivalent to 16.66%. Therefore, if B increases by 20%, C needs to decrease by 16.66% to keep A as a constant.
10.
Two successive discounts of 10% and 20% is equivalent to a single discount of 30%.
Correct Answer
B. False
Explanation
This statement is false. Two successive discounts of 10% and 20% are not equivalent to a single discount of 30%. When two discounts are applied successively, the total discount is calculated by subtracting the first discount from the original price and then subtracting the second discount from the discounted price. In this case, a 10% discount followed by a 20% discount would result in a total discount of 28%.
11.
If A gets 100% more than B, then by what percent B gets less than A?
Correct Answer
A. 50%
Explanation
If A gets 100% more than B, it means that A's amount is double the amount of B. In other words, A gets 100% of B's amount plus the original amount of B. Therefore, B gets 50% less than A because B's amount is half of A's amount.
12.
Ratio of A : B is 6:7. By what percent B is more than A?
Correct Answer
A. 16.66%
Explanation
The ratio of A to B is given as 6:7. To find the percentage by which B is more than A, we can use the formula: (B - A)/A * 100. Plugging in the values, we get (7 - 6)/6 * 100 = 16.66%. This means that B is 16.66% more than A.
13.
If the length of a rectangle is decreased by 20% and its breadth is increased by 5% then the area of the rectangle becomes 756 sq.cm. Find the area of the original rectangle.
Correct Answer
C. 900
Explanation
When the length of the rectangle is decreased by 20%, it becomes 80% of its original length. Similarly, when the breadth is increased by 5%, it becomes 105% of its original breadth. The area of a rectangle is calculated by multiplying its length and breadth. So, if we let the original length be L and the original breadth be B, we can write the equation: 0.8L * 1.05B = 756. Solving this equation, we find L * B = 900, which is the area of the original rectangle.
14.
( 20% of 16.66% of 9.09% of 25% of 1320 ) is what percent of (200% of 1)
Correct Answer
C. 50%
Explanation
To find the percentage, we need to calculate the value of 20% of 16.66% of 9.09% of 25% of 1320, which is 0.2 * 0.1666 * 0.0909 * 0.25 * 1320 = 7.5. Then, we need to calculate the value of 200% of 1, which is 2. Finally, we need to find what percentage 7.5 is of 2. By dividing 7.5 by 2 and multiplying by 100, we get 375. Therefore, 7.5 is 375% of 2. However, the question asks for the opposite - what percentage 7.5 is of 2. So, the answer is 50%.
15.
The length, Breadth, and Height of a cuboid are in the ratio 5:3:2. The volume of the cuboid is 100 m^{3}. If the length and breadth are doubled and height is halved, then what is the change in the volume of the cuboid?
Correct Answer
C. 100% increase
Explanation
When the length, breadth, and height of a cuboid are in the ratio 5:3:2, we can assume their values to be 5x, 3x, and 2x respectively. The volume of the cuboid is given as 100 m3, which can be calculated as (5x)(3x)(2x) = 100. Solving this equation, we find x = 2. Therefore, the dimensions of the cuboid are 10m, 6m, and 4m.
When the length and breadth are doubled and the height is halved, the new dimensions become 20m, 12m, and 2m. The new volume can be calculated as (20m)(12m)(2m) = 480m3.
Comparing the new volume (480m3) with the original volume (100m3), we can see that the volume has increased by 380m3. This increase represents a 380% increase in volume, which is equivalent to a 100% increase. Hence, the answer is 100% increase.