To solve this problem, we need to determine the number of notes of each denomination based on their given ratio and the total value. We will represent the number of notes using a common multiplier, calculate the total value in terms of this multiplier, and then solve for the multiplier. Finally, we will use the multiplier to find the number of Rs. 20 notes.
Define the number of notes:
The ratio of Rs. 10, Rs. 20, and Rs. 50 notes is 1:3:5. Let the common multiplier be \(x\).
Calculate the total value in terms of \(x\):
The value contributed by each denomination is its face value multiplied by the number of notes.
The total value in the bag is the sum of these values:
\[ \text{Total Value} = 10x + 60x + 250x = 320x \]Equate total value to the given amount:
We are given that the total value of money in the bag is Rs. 1920.
Solve for \(x\):
Divide both sides by 320 to find the value of \(x\).
Find the number of Rs. 20 notes:
The number of Rs. 20 notes is \(3x\).
Correct Option: C) 18
To express a fraction as a percentage, we first write the given numbers as a fraction (part/whole) and then multiply the result by 100%.
Identify the part and the whole: The question asks to write 95 out of 200 as a percentage. Here, 95 is the part and 200 is the whole.
Formulate the fraction: The fraction representing 95 out of 200 is:
\[ \frac{\text{Part}}{\text{Whole}} = \frac{95}{200} \]Convert the fraction to a percentage: To convert a fraction to a percentage, multiply it by 100%.
\[ \text{Percentage} = \left( \frac{95}{200} \right) \times 100\% \]Perform the calculation:
\[ \text{Percentage} = \frac{95}{2} \% \]\[ \text{Percentage} = 47.5\% \]Thus, 95 out of 200 is 47.5%.
Correct Option: B) 47.5%
The question asks to identify the historical figure known as the 'Lady with a lamp'. This nickname is associated with a prominent figure in the field of nursing, particularly during the Crimean War.
Correct Option: B) Florence Nightingale was a celebrated British nurse, social reformer, and statistician, best known as the founder of modern nursing. She rose to prominence during the Crimean War for organizing care for wounded soldiers. Her nocturnal rounds to check on patients, carrying a lamp, earned her the enduring nickname "The Lady with a Lamp."
The question asks to identify the type of change that rusting of iron represents. We need to understand the definitions of physical, chemical, exothermic, and endothermic changes to correctly classify rusting.
Correct Option: D) Chemical Change
This problem involves the relationship between distance, speed, and time. Since the distance to the school is constant, we can set up equations for the time taken at two different speeds and use the given time difference to find the distance.
Let the distance to the school be \(D\) km.
Let the speed be \(S_1 = 45\) kmph and \(S_2 = 60\) kmph.
The formula relating distance, speed, and time is: \[\text{Time} = \frac{\text{Distance}}{\text{Speed}}\]
When Lalitha drives at \(S_1 = 45\) kmph, the time taken is \(T_1 = \frac{D}{45}\) hours.
When Lalitha drives at \(S_2 = 60\) kmph, the time taken is \(T_2 = \frac{D}{60}\) hours.
We are given that she reaches 5 minutes later when driving at 45 kmph than when driving at 60 kmph. This means the difference in time is 5 minutes. Convert 5 minutes to hours: \[5 \text{ minutes} = \frac{5}{60} \text{ hours} = \frac{1}{12} \text{ hours}\]
So, we can write the equation: \[T_1 - T_2 = \frac{1}{12}\]
Substitute the expressions for \(T_1\) and \(T_2\): \[\frac{D}{45} - \frac{D}{60} = \frac{1}{12}\]
To solve for \(D\), find a common denominator for 45 and 60. The least common multiple (LCM) of 45 and 60 is 180.
Multiply both sides of the equation by 180: \[180 \left(\frac{D}{45} - \frac{D}{60}\right) = 180 \left(\frac{1}{12}\right)\] \[4D - 3D = 15\] \[D = 15\]
Therefore, the distance to her school is 15 km.
B) 15
The question asks about the authority responsible for resolving disputes related to the election of the President of India. This is a direct question about the constitutional provisions governing presidential elections.
Correct Option: D) The Supreme Court of India has the exclusive jurisdiction to inquire into and decide all doubts and disputes arising out of or in connection with the election of the President or Vice-President, and its decision is final. This is explicitly stated in Article 71(1) of the Constitution.
When three numbers are in proportion, it means that the ratio of the first to the second is equal to the ratio of the second to the third. This is also known as continued proportion or mean proportion. If numbers \(a, b, c\) are in proportion, then \[\frac{a}{b} = \frac{b}{c}\].
D) 0.65 is the correct value for X, as calculated by applying the definition of proportion.
The question asks for the signing year of the Indus Water Treaty between India and Pakistan. This is a factual question requiring knowledge of historical international agreements.
D) 1960 — The Indus Water Treaty was signed on September 19, 1960, in Karachi by the then Prime Minister of India, Jawaharlal Nehru, and President of Pakistan, Ayub Khan.
Girish can paint a picture in 4 days when he works for 8 hours per day. Due to illness, he could work for only 6 hours per day and was required to finish painting 7 such pictures. How many days would Girish take to finish the work?
This problem involves calculating the total work required and then determining the number of days needed to complete that work under changed conditions. We will first find the total work in terms of man-hours for one picture, then for seven pictures, and finally divide by the new daily working hours to find the number of days.
B) \( 37 \frac{1}{3} \) is the correct answer. This matches our calculation for the total number of days Girish would take to finish painting 7 pictures working 6 hours per day.
This is a logical reasoning question where we must evaluate conclusions based solely on the given statements, without introducing outside knowledge. We need to determine which conclusions logically follow from the provided statements.
Correct Option: B) Only II follows.