To find the new value when a number is increased by a certain percentage, we first calculate the percentage increase amount and then add it to the original number. Alternatively, we can directly calculate the new value by multiplying the original number by \((1 + \text{percentage increase as a decimal})\).
Original number \( = 5650 \)
Percentage increase \( = 15\% \)
First, calculate \(15\%\) of \(5650\):
\[ \text{Increase amount} = 15\% \text{ of } 5650 = \frac{15}{100} \times 5650 \] \[ \text{Increase amount} = 0.15 \times 5650 = 847.50 \]Now, add this increase amount to the original number:
\[ \text{New value} = \text{Original number} + \text{Increase amount} \] \[ \text{New value} = 5650 + 847.50 = 6497.50 \]The new value will be \(100\% + 15\% = 115\%\) of the original number.
Convert the percentage to a decimal: \(115\% = 1.15\)
\[ \text{New value} = \text{Original number} \times (1 + \text{percentage increase as decimal}) \] \[ \text{New value} = 5650 \times (1 + 0.15) \] \[ \text{New value} = 5650 \times 1.15 \] \[ \text{New value} = 6497.50 \]Both methods yield the same result.
Correct Option: D) 6497.50
This problem involves a dishonest shopkeeper who claims to sell at cost price but uses a faulty weight to gain profit. We need to find the actual weight given for every kilogram paid for by the customer. The key is to relate the percentage gain to the difference between the true weight and the false weight used.
The percentage gain for a dishonest shopkeeper is given by:
\[ \text{Gain percentage} = \frac{\text{Error}}{\text{True weight} - \text{Error}} \times 100 \]Here, \(\text{Error} = \text{True weight} - \text{False weight}\).
So, the formula can be rewritten as:
\[ \text{Gain percentage} = \frac{\text{True weight} - \text{False weight}}{\text{False weight}} \times 100 \]Rounding 877.19 gm to the nearest whole number gives 877 gm.
Correct Option: B) 877 gm
The given series is 200, 119, 70, 45, 36, ?. We need to identify the pattern in the series by finding the differences between consecutive terms and then apply that pattern to find the missing number.
The differences are 81, 49, 25, 9.
Observe that these differences are perfect squares:
The pattern of the bases of these squares is a decreasing sequence of odd numbers: 9, 7, 5, 3.
Following the pattern of odd numbers, the next odd number after 3 is 1. So, the next difference should be \(1^2\).
\[ 1^2 = 1 \]The series is decreasing, so we subtract the next difference from the last known term (36).
\[ 36 - 1 = 35 \]D) 35 is the correct answer because the pattern of differences between consecutive terms is a sequence of decreasing odd squares (\(9^2, 7^2, 5^2, 3^2, 1^2\)).
Veer starts from Point A and drives 7 km towards the north. He then takes a right turn, drives 8 km, turns right and drives 19 km. He then takes a right turn and drives 3 km, takes a right turn and drives 12 km and stops at Point B. How far and towards which direction should he drive in order to reach Point A from Point B? (All turns are 90-degree turns only.)
8 km towards the south
9 km towards the south
5 km towards the west
6 km towards the east
This problem involves tracking movement in different directions. We can solve it by breaking down Veer's journey into components along the North-South and East-West axes. We'll calculate the net displacement in each direction from the starting point (Point A) to the final point (Point B) and then determine the distance and direction required to return to Point A.
C) 5 km towards the west
From the calculations, Point B is 5 km to the East of Point A. Therefore, to reach Point A from Point B, Veer must drive 5 km towards the West.
The problem presents an analogy where a certain mathematical relationship exists between pairs of numbers. We need to identify this relationship and apply it to the incomplete pair to find the missing number.
A) 4 is the correct answer because the established pattern \((X/9) \times 2 = Y\) holds true for all given pairs.
To solve this problem, we first need to arrange the given numbers in descending order. Then, we identify the second number from the right and the fifth number from the left in this new arrangement. Finally, we calculate their sum.
The numbers are: \(106, 91, 131, 95, 144, 123, 88, 93, 127, 73\).
Descending order means arranging from the largest to the smallest.
The sorted list is: \(144, 131, 127, 123, 106, 95, 93, 91, 88, 73\).
In the descending order list:
In the descending order list:
Sum \( = \text{Second number from right} + \text{Fifth number from left}\)
Sum \( = 88 + 106\)
Sum \( = 194\)
C) 194 is the correct sum of the second number from the right (88) and the fifth number from the left (106) after arranging the numbers in descending order.
To answer this question, we need to recall the definition of a combination reaction in chemistry. A combination reaction is a type of chemical reaction where two or more reactants combine to form a single, more complex product.
Correct Option: C) A single product is formed from two or more reactants.
The question asks about a specific policy change made by the Government of India in 2014 regarding the validity period of industrial licenses. To answer this, one needs to recall the economic reforms or policy announcements related to industrial licensing during that period, specifically those aimed at boosting domestic manufacturing.
Correct Option: D) seven — In 2014, the Government of India extended the validity of industrial licenses from three years to seven years as part of its efforts to encourage domestic manufacturing and improve the ease of doing business, aligning with the 'Make in India' initiative.
The question asks for a general proof of being alive, which means identifying the fundamental characteristics common to all living organisms. We need to evaluate each option based on the universally accepted criteria for life.
D) Related to any kind of movement, growth or respiration. This option provides a comprehensive and accurate set of fundamental characteristics that are universally associated with being alive. All living organisms, from the simplest bacteria to complex animals and plants, exhibit some form of movement, growth, and respiration (metabolism).
The question asks about the categorization of Municipalities under Article 243Q of the Indian Constitution. To answer this, we need to recall the provisions of this specific article, which was introduced by the 74th Constitutional Amendment Act.
Correct Option: B) Three