To find the single equivalent discount for successive discounts, we can assume an original price (e.g., Rs. 100) and calculate the price after each discount. Alternatively, we can use a direct formula for equivalent discount.
Method 1: Assuming an original price
Let the original price of the item be Rs. 100.
First discount is 40%.
\[ \text{Price after first discount} = 100 - (40\% \text{ of } 100) = 100 - 40 = \text{Rs. } 60 \]Second discount is 60% on the discounted price (Rs. 60).
\[ \text{Discount amount} = 60\% \text{ of } 60 = \frac{60}{100} \times 60 = 36 \]Price after second discount:
\[ \text{Final Price} = 60 - 36 = \text{Rs. } 24 \]Total discount given from the original price:
\[ \text{Total Discount} = \text{Original Price} - \text{Final Price} = 100 - 24 = \text{Rs. } 76 \]Since the original price was Rs. 100, the equivalent single discount is 76%.
Method 2: Using the equivalent discount formula
For two successive discounts of \(d_1\%\) and \(d_2\%\), the single equivalent discount is given by the formula:
\[ \text{Equivalent Discount} = \left(d_1 + d_2 - \frac{d_1 \times d_2}{100}\right)\% \]Given discounts are \(d_1 = 40\%\) and \(d_2 = 60\%\).
Substitute the values into the formula:
\[ \text{Equivalent Discount} = \left(40 + 60 - \frac{40 \times 60}{100}\right)\% \] \[ \text{Equivalent Discount} = \left(100 - \frac{2400}{100}\right)\% \] \[ \text{Equivalent Discount} = (100 - 24)\% \] \[ \text{Equivalent Discount} = 76\% \]C) 76% is the correct equivalent single discount.
A) 70% ā This would be incorrect. It might be obtained by some miscalculation or by incorrectly averaging the discounts.
B) 66% ā This is incorrect. It does not account for the compounding nature of successive discounts.
D) 80% ā This would be incorrect. It might be obtained by simply adding the discounts and then subtracting a fixed percentage, which is not the correct method for successive discounts.
To simplify the given algebraic expression, we will expand the squared terms using the algebraic identity \((a-b)^2 = a^2 - 2ab + b^2\) and \((a+b)^2 = a^2 + 2ab + b^2\). After expanding, we will combine like terms to arrive at the simplified expression.
Using the identity \((a-b)^2 = a^2 - 2ab + b^2\), where \(a = 2z\) and \(b = 5y\):
\[ (2z - 5y)^2 = (2z)^2 - 2(2z)(5y) + (5y)^2 \]\[ = 4z^2 - 20zy + 25y^2 \]Using the identity \((a+b)^2 = a^2 + 2ab + b^2\), where \(a = 5z\) and \(b = 2y\):
\[ (5z + 2y)^2 = (5z)^2 + 2(5z)(2y) + (2y)^2 \]\[ = 25z^2 + 20zy + 4y^2 \]The original expression is \((2z - 5y)^2 + (5z + 2y)^2 - 25z^2\).
Substitute the expanded forms from steps 1 and 2:
\[ (4z^2 - 20zy + 25y^2) + (25z^2 + 20zy + 4y^2) - 25z^2 \]Group the terms with \(z^2\), \(zy\), and \(y^2\) together:
\[ (4z^2 + 25z^2 - 25z^2) + (-20zy + 20zy) + (25y^2 + 4y^2) \]Simplify each group:
Adding these simplified parts gives:
\[ 4z^2 + 0 + 29y^2 = 4z^2 + 29y^2 \]This can also be written as \(29y^2 + 4z^2\).
C) \(29y^2 + 4z^2\) is the correct simplified expression, as derived in the step-by-step solution.
To find the Least Common Multiple (LCM) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then multiplying the highest powers of all unique prime factors together.
D) 420 is the correct LCM of 84, 105, and 140.
This question tests the understanding of fundamental concepts in physics, specifically Newton's laws of motion and inertia. The scenario described is a classic example used to illustrate the principle of inertia.
C) the inertia of our body ā Inertia is the property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force. When the bus stops suddenly, your body, due to its inertia, tends to continue moving forward at the bus's previous speed, causing you to lurch forward.
The question asks to identify the Sustainable Development Goal (SDG) that requires targeted efforts according to NITI Aayog's SDG India Index 2023ā24, specifically those with a score below 50. This requires knowledge of the findings of the NITI Aayog's report.
Correct Option: A) Goal 5 (Gender Equality) is highlighted in the NITI Aayog's SDG India Index 2023ā24 as needing targeted efforts due to its score being below 50. This goal consistently shows significant challenges across various indicators related to gender equality.
To find the number of bricks required, we need to calculate the effective volume of the wall that needs to be filled with bricks, considering the mortar. First, convert all dimensions to a consistent unit (cm). Then, calculate the volume of the wall and the volume of one brick. Subtract the volume occupied by mortar from the total wall volume to get the volume to be filled by bricks. Finally, divide the brick-filled volume of the wall by the volume of a single brick.
10% of the wall is filled with mortar.
\[ V_{\text{mortar}} = 10\% \text{ of } V_{\text{wall}} \]\[ V_{\text{mortar}} = \frac{10}{100} \times 115,200,000 \text{ cm}^3 \]\[ V_{\text{mortar}} = 11,520,000 \text{ cm}^3 \]Correct Option: A) 45000
This question tests knowledge about the reproductive parts of a flower and the process of fertilisation in plants. We need to identify the statement that incorrectly describes these biological processes or structures.
Correct Option: B) Female gamete is present in the stigma.
Given below is a statement followed by two possible reasons numbered I and II. Read the statement carefully and decide which of the two explain(s) the event/observation/information given in the statement.
Statement - The railway authorities have decided to run two holiday special trains on Tuesdays and Fridays from City A to City B from 19th October 2023 to 5th January 2024.
Reasons:
(I) Flights from City A to City C are booked to capacity, and airlines are planning to increase the number of flights operating between City A and City C from August 2023.
(II) Many migrants from City B who work in City A, travel back to City B on trains from October to January for the festivals. The existing trains cannot accommodate this increase in passenger demand.
Neither I nor II is a possible reason.
Only I is a possible reason.
Only II is a possible reason.
Both I and II are possible reasons.
The problem asks us to identify which of the given reasons logically explains the railway authorities' decision to run special holiday trains. We need to evaluate each reason's relevance and direct connection to the statement.
C) Only II is a possible reason. This reason directly explains the need for additional trains between City A and City B during the specified festive period due to increased passenger demand from migrants returning home for festivals.
The problem describes a relationship between two sets of letters based on their positions in the English alphabet. We need to identify the pattern in the given examples and then apply the same pattern to find the related term for "STIX".
Let's find the positional value of each letter in the alphabet (A=1, B=2, ..., Z=26).
The pattern for the first pair is: \((+2, -2, +3, -3)\).
Let's check if the same pattern applies:
The pattern \((+2, -2, +3, -3)\) is consistent.
Now, let's apply the pattern \((+2, -2, +3, -3)\) to the word STIX:
So, STIX is related to URLU.
B) URLU is the correct option as it follows the established pattern \((+2, -2, +3, -3)\).
The question asks for the total number of Arjuna Awards conferred during the National Sports Awards 2023. This requires factual knowledge about the awards announced for that specific year.
Correct Option: C) 26. A total of 26 sportspersons were conferred with the Arjuna Awards during the National Sports Awards 2023. These awards recognize outstanding performance in sports and games.