This problem involves a percentage increase in the price of rice and a corresponding decrease in the quantity purchased for a fixed amount of money. We need to find the original (old) rate per kg. We can set up an equation relating the old rate, new rate, old quantity, and new quantity, using the given information that the quantity decreases by 3 kg.
Let the old rate of rice be \(\text{₹}x\) per kg.
The rate increases by 20%. So, the new rate will be:
\[ \text{New Rate} = x + 0.20x = 1.20x \text{ per kg} \]The total amount spent is ₹630. At the old rate, the quantity of rice purchased would be:
\[ \text{Old Quantity} = \frac{\text{Total Amount}}{\text{Old Rate}} = \frac{630}{x} \text{ kg} \]At the new rate, the quantity of rice purchased is:
\[ \text{New Quantity} = \frac{\text{Total Amount}}{\text{New Rate}} = \frac{630}{1.20x} \text{ kg} \]According to the problem, the man gets 3 kg less at the new rate compared to the old rate. So, the difference between the old quantity and the new quantity is 3 kg:
\[ \text{Old Quantity} - \text{New Quantity} = 3 \]\[ \frac{630}{x} - \frac{630}{1.20x} = 3 \]Now, solve the equation for \(x\):
\[ 630 \left( \frac{1}{x} - \frac{1}{1.20x} \right) = 3 \]\[ 630 \left( \frac{1.20 - 1}{1.20x} \right) = 3 \]\[ 630 \left( \frac{0.20}{1.20x} \right) = 3 \]\[ 630 \left( \frac{1}{6x} \right) = 3 \]\[ \frac{105}{x} = 3 \]\[ x = \frac{105}{3} \]\[ x = 35 \]Therefore, the old rate of that variety of rice is ₹35 per kg.
B) ₹35 per kg is the correct answer, as calculated from the equation.
This question tests general knowledge about major international sporting events. Specifically, it asks about the host city of the Special Olympics World Games in a particular year. To answer this, one needs to recall the location of the 2019 event.
Correct Option: A) Abu Dhabi, UAE
The Special Olympics World Summer Games 2019 were indeed held in Abu Dhabi, United Arab Emirates, from March 14 to March 21, 2019. It was the first time the event was held in the Middle East/North Africa region.
The problem involves calculating the initial number of boys and girls based on a given total and ratio. Then, we need to update the number of girls after new enrollments and finally determine the new ratio of boys to girls.
Correct Option: A) 35 : 27
The problem asks us to identify the odd pair out of four given options. We need to find a common relationship that holds true for three pairs and identify the pair that does not follow this relationship.
Correct Option: D) Dogs : Coop
The question asks for the definition of oxidation. We need to recall the various definitions of oxidation in chemistry, which include the gain of oxygen, loss of hydrogen, and loss of electrons.
Correct Option: B) A substance gaining oxygen during a chemical reaction
To find the net percentage effect on daily sale, we need to consider how changes in price and sale volume interact. We can assume initial values for price and daily sale to make calculations easier, or use a direct formula for successive percentage changes. The total daily revenue (or sale value) is the product of price and daily sale quantity. We will calculate the initial total daily sale and the new total daily sale after the changes, then find the percentage change.
Let the original price of the article be \(P = 100\).
Let the original daily sale quantity be \(Q = 100\).
The original total daily sale (revenue) would be \(R_{\text{original}} = P \times Q = 100 \times 100 = 10000\).
The price was reduced by 15%.
\[ P_{\text{new}} = P - (0.15 \times P) = 100 - (0.15 \times 100) = 100 - 15 = 85 \]The daily sale increased by 25%.
\[ Q_{\text{new}} = Q + (0.25 \times Q) = 100 + (0.25 \times 100) = 100 + 25 = 125 \]The new total daily sale (revenue) is:
\[ R_{\text{new}} = P_{\text{new}} \times Q_{\text{new}} = 85 \times 125 \]\[ R_{\text{new}} = 10625 \]The net percentage effect is the percentage change from the original total daily sale to the new total daily sale.
\[ \text{Percentage Change} = \frac{R_{\text{new}} - R_{\text{original}}}{R_{\text{original}}} \times 100 \]\[ \text{Percentage Change} = \frac{10625 - 10000}{10000} \times 100 \]\[ \text{Percentage Change} = \frac{625}{10000} \times 100 \]\[ \text{Percentage Change} = 0.0625 \times 100 \]\[ \text{Percentage Change} = 6.25\% \]Since the value is positive, it is an increase.D) 6.25 % increase
To solve this problem, we need to determine the angular speed of the Earth's rotation. We know that the Earth completes one full rotation (360°) in 24 hours. We will first convert the given time (5 hours and 24 minutes) entirely into hours or minutes, and then use a proportion to find the angle turned.
The Earth rotates \(360^\circ\) in 24 hours.
Given time = 5 hours and 24 minutes.
Convert minutes to hours:
\[ 24 \text{ min} = \frac{24}{60} \text{ h} = \frac{2}{5} \text{ h} = 0.4 \text{ h} \]Total time in hours:
\[ 5 \text{ h} + 0.4 \text{ h} = 5.4 \text{ h} \]We can set up a proportion:
\[ \frac{\text{Angle turned}}{\text{Time taken}} = \frac{\text{Total angle of rotation}}{\text{Total time for one rotation}} \]Let \(\theta\) be the angle turned in 5.4 hours.
\[ \frac{\theta}{5.4 \text{ h}} = \frac{360^\circ}{24 \text{ h}} \]Now, solve for \(\theta\):
\[ \theta = \frac{360^\circ}{24 \text{ h}} \times 5.4 \text{ h} \] \[ \theta = 15^\circ/\text{h} \times 5.4 \text{ h} \] \[ \theta = 81^\circ \]Correct Option: B) 81°
To find the ratio \(X:W\), we can multiply the given ratios in a chain. This method allows us to cancel out intermediate variables (Y and Z) and directly relate X to W.
Write down the given ratios as fractions:
Multiply these fractions together:
\[ \frac{X}{Y} \times \frac{Y}{Z} \times \frac{Z}{W} \]Substitute the given values into the multiplication:
\[ \frac{X}{W} = \frac{4}{5} \times \frac{5}{7} \times \frac{7}{9} \]Cancel out the common terms (Y and Z) from the numerator and denominator:
\[ \frac{X}{W} = \frac{4}{\cancel{5}} \times \frac{\cancel{5}}{\cancel{7}} \times \frac{\cancel{7}}{9} \]Perform the multiplication of the remaining terms:
\[ \frac{X}{W} = \frac{4}{9} \]Express the result as a ratio:
\(X : W = 4 : 9\)
A) \(4 : 9\) is the correct ratio obtained by multiplying the given ratios.
To solve this problem, we need to determine a common value that, when subtracted from both terms of the initial ratio (17:21), results in the new ratio (7:9). We can set up an algebraic equation to represent this relationship and then solve for the unknown value.
A) 3 is the correct answer because when 3 is subtracted from both terms of the ratio 17:21, it becomes 14:18, which simplifies to 7:9.
The question asks to identify the Indian personality who was awarded the Nobel Peace Prize in 2014. This requires knowledge of Nobel laureates from India and their respective fields and years of award.
Kailash Satyarthi, an Indian children's rights advocate, was awarded the Nobel Peace Prize in 2014, jointly with Malala Yousafzai, for his struggle against the suppression of children and young people and for the right of all children to education.
Correct Option: C) Kailash Satyarthi