Percentage is one of the most common topics in quantitative aptitude tests, especially for psc exams. PSC aspirants need to master the concepts and formulas of percentage to solve various types of problems quickly and accurately. In this blog post, we will discuss some important percentage questions and answers that helpful for psc aspirants.
Question 1: What is the percentage increase in the area of a rectangle if its length is increased by 20% and its breadth is decreased by 10%?
Answer: Let the original length and breadth of the rectangle be L and B respectively. Then, the original area of the rectangle is L x B. After the changes, the new length and breadth of the rectangle are 1.2L and 0.9B respectively. Then, the new area of the rectangle is 1.2L x 0.9B = 1.08LB. The percentage increase in the area of the rectangle is given by:
((New area - Original area) / Original area) x 100
= ((1.08LB - LB) / LB) x 100
= (0.08LB / LB) x 100
= 8%
Therefore, the percentage increase in the area of the rectangle is 8%.
Question 2: A student scored 75% marks in an exam. If he scored 45 marks more, his percentage would have been 85%. How many marks did he score in the exam?
Answer: Let the total marks in the exam be M. Then, the student scored 75% of M, which is equal to 0.75M. If he scored 45 marks more, his percentage would have been 85%, which is equal to 0.85M. Therefore, we have:
0.75M + 45 = 0.85M
=> 0.1M = 45
=> M = 450
Therefore, the total marks in the exam were 450. The student scored 75% of 450, which is equal to:
0.75 x 450 = 337.5
Therefore, the student scored 337.5 marks in the exam.
Question 3: A jar contains a mixture of milk and water in the ratio of 5:3. If 16 liters of water are added to the jar, the ratio becomes 5:4. What is the capacity of the jar?
Answer: Let the original quantity of milk and water in the jar be 5x and 3x liters respectively. Then, the capacity of the jar is (5x + 3x) liters, which is equal to 8x liters. After adding 16 liters of water, the quantity of water becomes (3x + 16) liters, and the ratio of milk and water becomes 5:4. Therefore, we have:
(5x / (3x + 16)) = (5 / 4)
=> (20x / (12x + 64)) = (5 /4)
=> (80x / (48x +256)) = (5 /4)
=> (80x -200x) = (48x +256)
=> (-120x) = (48x +256)
=> (-168x) = (256)
=> x = (-256 /168)
=> x = (-1.52)
Since x cannot be negative, we reject this value.
Therefore, there is no such jar that satisfies the given conditions.
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