The problem asks us to find the percentage profit if no discount is given. We are provided with the selling price after a discount, the discount percentage, and the profit percentage earned under these conditions. We will first calculate the Marked Price (MP) using the Selling Price (SP) and discount. Then, we will find the Cost Price (CP) using the SP and profit percentage. Finally, we will calculate the new profit percentage if the article is sold at the Marked Price (no discount).
The shopkeeper sells 25 articles at Rs 45 per article. So, the selling price of one article is Rs 45.
\[ \text{SP} = \text{Rs } 45 \]A 10% discount is given on the Marked Price. This means the Selling Price is 90% of the Marked Price.
\[ \text{SP} = \text{MP} - (10\% \text{ of MP}) \]\[ \text{SP} = \text{MP} \times (1 - 0.10) \]\[ 45 = \text{MP} \times 0.90 \]\[ \text{MP} = \frac{45}{0.90} \]\[ \text{MP} = \text{Rs } 50 \]The shopkeeper earns a 50% profit after giving the discount. This profit is calculated on the Cost Price. So, the Selling Price (Rs 45) is 150% of the Cost Price.
\[ \text{SP} = \text{CP} + (50\% \text{ of CP}) \]\[ \text{SP} = \text{CP} \times (1 + 0.50) \]\[ 45 = \text{CP} \times 1.50 \]\[ \text{CP} = \frac{45}{1.50} \]\[ \text{CP} = \text{Rs } 30 \]If no discount is given, the article is sold at its Marked Price (MP). So, the new Selling Price will be Rs 50.
New Profit = New SP - CP
\[ \text{New Profit} = 50 - 30 \]\[ \text{New Profit} = \text{Rs } 20 \]Profit percentage is calculated on the Cost Price.
\[ \text{Profit Percentage} = \left( \frac{\text{New Profit}}{\text{CP}} \right) \times 100 \]\[ \text{Profit Percentage} = \left( \frac{20}{30} \right) \times 100 \]\[ \text{Profit Percentage} = \left( \frac{2}{3} \right) \times 100 \]\[ \text{Profit Percentage} = 0.6666... \times 100 \]\[ \text{Profit Percentage} = 66.666...\% \]Correct Option: C) 66.67%
This problem involves calculating ages at different points in time (past, present, and future) using average age information. We will set up equations based on the given averages and solve for the current ages, then determine B's age three years from now.
Given that the average age of A, B, and C five years ago was 35 years.
\[ \ \text{Sum of ages} = \text{Average age} \times \text{Number of people} \ \]\[ \ (A - 5) + (B - 5) + (C - 5) = 35 \times 3 \ \]\[ \ A + B + C - 15 = 105 \ \]\[ \ A + B + C = 105 + 15 \ \]\[ \ A + B + C = 120 \quad \text{(Equation 1: Sum of present ages of A, B, C)} \ \]Given that the average age of A and C five years from now will be 48 years.
\[ \ (A + 5) + (C + 5) = 48 \times 2 \ \]\[ \ A + C + 10 = 96 \ \]\[ \ A + C = 96 - 10 \ \]\[ \ A + C = 86 \quad \text{(Equation 2: Sum of present ages of A and C)} \ \]Substitute Equation 2 into Equation 1:
\[ \ (A + C) + B = 120 \ \]\[ \ 86 + B = 120 \ \]\[ \ B = 120 - 86 \ \]\[ \ B = 34 \quad \text{(Present age of B)} \ \]B's age three years from now will be:
\[ \ \text{B's age (3 years from now)} = \text{Present age of B} + 3 \ \]\[ \ = 34 + 3 \ \]\[ \ = 37 \ \]C) 37 — Based on our calculations, B's present age is 34 years, and three years from now, B will be 37 years old.
The question asks to identify the factor that does NOT directly affect India's climate. We need to evaluate each option based on its known influence on climatic conditions in India.
Correct Option: C) Snowfall in European countries does not directly affect the climate of India. India's climate is primarily shaped by factors like its latitudinal extent, altitude, pressure and wind systems (especially the monsoon), distance from the sea, ocean currents, and relief features.
The question asks to identify a material whose electrical resistance remains almost unaffected by changes in temperature. This property is characteristic of certain alloys used in precision electrical components.
Manganin is an alloy primarily composed of copper (about 86%), manganese (about 12%), and nickel (about 2%). It is specifically known for having a very low temperature coefficient of resistance. This means its electrical resistance changes very little with variations in temperature. Due to this property, manganin is widely used in the manufacturing of precision resistors, resistance boxes, and other electrical components where stable resistance is crucial, such as in measuring instruments.
To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. We will analyze the differences between consecutive terms to determine if there's an arithmetic progression, a pattern in the differences, or another mathematical relationship.
D) 76 — The pattern of differences between consecutive terms is a sequence of prime numbers (5, 7, 11, 13, ...). The next prime number after 13 is 17. Adding 17 to the last term (59) gives \(59 + 17 = 76\).
The question asks to identify the correct statements regarding the emphasis of watershed management. We need to evaluate each given statement based on the principles and objectives of watershed management.
Correct Option: B) a, b and c
We need to determine the seating arrangement of six students around a circular table based on the given clues. We will place students one by one using the definite information and then deduce the positions of the remaining students.
If C is at position 1, then second to its left (clockwise direction for facing center) would be position 3. So, A is at position 3.
_ _ C _ _ A (where C is at 1, A is at 3, and _ are empty seats)
From Clue 2, we have C and A with one person in between. If R is an immediate neighbour of both A and C, then R must be in the seat between C and A. So, the arrangement becomes:
_ R C _ _ A (where C is at 1, R is at 6, A is at 3)
From Clue 1, Q is an immediate neighbour of C. Since R is already to the left of C, Q must be to the right of C. So, Q is at position 2.
_ R C Q _ A (where C is at 1, Q is at 2, A is at 3, R is at 6)
_ R C Q B A (where C is at 1, Q is at 2, B is at 3, A is at 4, R is at 6)
Wait, this conflicts with A being at position 3. Let's re-evaluate the left/right for circular arrangement.
Let's draw it:
Assume C is at the top (12 o'clock position).
Arrangement so far: C - R - A (clockwise). This means if C is at 1, R is at 2, A is at 3.
Since R is to the right of C, Q must be to the left of C (anti-clockwise). So, C - Q - B (anti-clockwise).
Let's place C. Then A is 2nd to the left of C. R is between C and A. This means the sequence is C-R-A (clockwise if left is clockwise). So, if C is at 1, R is at 2, A is at 3.
Now, Q is an immediate neighbour of C. Since R is already on one side of C, Q must be on the other side. So, Q is to the left of C (anti-clockwise from C). Let's say C is at position 1. R is at position 2. A is at position 3. Q is at position 6 (left of C).
Current arrangement: A _ _ C Q R (clockwise from A)
Positions: C (1), R (2), A (3), _ (4), _ (5), Q (6)
Current arrangement: A _ B C Q R (clockwise from A)
Positions: C (1), R (2), A (3), _ (4), B (5), Q (6)
Q is at position 6. Second to the right of Q (anti-clockwise) would be position 4. So P is at position 4.
Final arrangement (clockwise from C): C - R - A - P - B - Q
Let's verify all conditions:
The final arrangement (clockwise) is: C, R, A, P, B, Q.
We need to find who is an immediate neighbour of both A and B.
Looking at the arrangement: A is followed by P, and P is followed by B. So, P is between A and B.
A) P is an immediate neighbour of both A and B, as per our final arrangement (C, R, A, P, B, Q).
The question asks for the time taken to build India's first 3D printed house at IIT Madras, which was inaugurated by Union Finance Minister Nirmala Sitharaman on April 27, 2021. This is a factual recall question related to a significant technological advancement in India.
D) 5 days. The country's first 3D printed house, inaugurated at IIT Madras on April 27, 2021, was built in just 5 days by Tvasta Manufacturing Solutions.
To solve this problem, we need to track Asmita's movements step-by-step, considering each turn and distance covered. We can visualize her path using a coordinate system or by drawing a simple diagram. We will determine her final position relative to her starting point (the medicine shop) by calculating the net displacement in the East-West and North-South directions.
Starting Point: Let the medicine shop be the origin \((0,0)\).
First Movement: Asmita walks 400 metres south from the medicine shop. Her position is now \((0, -400)\).
Second Movement: She turns right. Since she was facing south, a right turn means she is now facing west. She walks 100 metres west. Her position is now \((-100, -400)\).
Third Movement: From the ice-cream parlour, she turns right. Since she was facing west, a right turn means she is now facing north. She walks 500 metres north. Her position is now \((-100, -400 + 500) = (-100, 100)\).
Fourth Movement: She again turns right. Since she was facing north, a right turn means she is now facing east. She walks 200 metres east to reach the vegetable shop. Her position is now \((-100 + 200, 100) = (100, 100)\).
Fifth Movement: Finally, she turns right. Since she was facing east, a right turn means she is now facing south. She walks 100 metres south to reach her home. Her final position is now \((100, 100 - 100) = (100, 0)\).
Final Position relative to Medicine Shop: Her home is at \((100, 0)\) and the medicine shop is at \((0,0)\). This means her home is 100 metres to the east of the medicine shop.
Correct Option: B) 100 metres east