1.
The length of the rectangle increases by 50%. Find the percentage decrease in breadth in order to maintain the area constantly.
Correct Answer
B. 33.33%
Explanation
When the length of a rectangle increases by 50%, the new length becomes 1.5 times the original length. To maintain the area constant, the product of the length and breadth should remain the same. Let's assume the original breadth is 100. So, the original area is 100 * original length. After the length increases by 50%, the new area should also be 100 * original length. So, the new breadth can be calculated by dividing the new area by the new length. The new breadth is (100 * original length) / (1.5 * original length) = 100/1.5 = 66.67. The percentage decrease in breadth is (100 - 66.67)/100 * 100 = 33.33%.
2.
The length of the rectangle decreases by 16.66%. Find the percentage increase in breadth in order to maintain the area constantly.
Correct Answer
A. 20%
Explanation
To maintain the area of a rectangle constant, when the length decreases by 16.66%, the breadth needs to increase by a certain percentage. The percentage increase in breadth can be calculated by dividing the percentage decrease in length by the original length and then multiplying by 100. In this case, since the length decreases by 16.66%, the percentage increase in breadth would be 16.66% divided by the original length (which is not given in the question) multiplied by 100. Therefore, the correct answer cannot be determined with the information provided.
3.
The area of a triangle is constant. Find the percentage increase in its perpendicular height if the base of the triangle is decreased by 50%.
Correct Answer
B. 100%
Explanation
When the base of a triangle is decreased by 50%, the area of the triangle remains constant. This means that the product of the base and the perpendicular height remains the same. Since the base is decreased by 50%, the perpendicular height must increase by 100% in order to maintain the same area. Therefore, the percentage increase in the perpendicular height is 100%.
4.
A = B * C
If B increases by 1/3, C decreases by ______
Given that A = Constant
Correct Answer
A. 1/4
Explanation
If B increases by 1/3, it means B is now 4/3 times its original value. Since A is constant, it means A must remain the same after the change. Therefore, in order for A to remain the same, C must decrease by 1/4 to compensate for the increase in B.
5.
If A = B * C
A = Constant
B decreases by 2/7. C increases by _____
Correct Answer
C. 2/5
Explanation
If A = B * C and A is constant, it means that the product of B and C must remain constant as well. Since B decreases by 2/7, C should increase by a value that compensates for this decrease in order to keep the product constant. The only option that satisfies this condition is 2/5, as increasing C by this value would offset the decrease in B by 2/7 and maintain the constant value of A.
6.
The percentage increase from A to B is 100%. Find the percentage decrease from B to A.
Correct Answer
B. 50%
Explanation
The percentage increase from A to B is 100%, which means that B is double the value of A. Therefore, to find the percentage decrease from B to A, we need to determine how much B needs to decrease in order to become equal to A. Since B is double the value of A, it needs to decrease by 50% to become equal to A.
7.
The salary of A is double that of the salary of B.
Salary of B is lesser than the salary of A by _____
Correct Answer
A. 50%
Explanation
The salary of B is lesser than the salary of A by 50%. This means that B's salary is half of A's salary.
8.
The price of wheat increased by 10 %. By how much percent should a mother reduce her consumption in the house so that her expenditure on wheat does not increase?
Correct Answer
B. 9.09%
Explanation
If the price of wheat increases by 10%, the mother would need to reduce her consumption by 9.09% in order to keep her expenditure on wheat from increasing. This is because a 10% increase in price would result in a 11.11% increase in expenditure, so reducing consumption by 9.09% would offset this increase and keep the expenditure the same.
9.
The salary of a doctor is increased by 40 %. By what per cent should the new salary be reduced in order to restore the original salary?
Correct Answer
A. 28.5%
Explanation
To restore the original salary after a 40% increase, the new salary needs to be reduced by a certain percentage. Let's assume the original salary is 100. After a 40% increase, the new salary becomes 140. To bring it back to the original 100, we need to find the percentage reduction from 140 to 100. This can be calculated by finding the difference between 140 and 100, which is 40, and then finding what percentage 40 is of 140. This comes out to be approximately 28.5%. Therefore, the new salary needs to be reduced by 28.5% to restore the original salary.
10.
A>B
Percentage increase from B to A is x and percentage decrease from A to B is y.
Which of the following is true?
Correct Answer
B. X > y
Explanation
The answer is x > y because the percentage increase from B to A is greater than the percentage decrease from A to B. This means that the difference between A and B is larger when A increases compared to when A decreases. Therefore, the percentage increase is greater than the percentage decrease.