A shopkeeper sells an item for ₹571.20 after giving two successive discounts of 20% and 15% on its marked price. Had he not given any discount, he would have earned a profit of 12%. What is the cost price (in ₹) of the item?
We need to find the cost price of the item. We are given the selling price after two successive discounts and the profit percentage if no discount was given. We will first find the marked price using the selling price and discounts. Then, using the marked price as the selling price without discount and the given profit percentage, we can calculate the cost price.
Let the marked price be \( \text{MP} \). The first discount is 20%, and the second is 15%.
Selling Price \[\text{SP} = \text{MP} \times \left(1 - \frac{20}{100}\right) \times \left(1 - \frac{15}{100}\right)\]
\[ \text{SP} = \text{MP} \times \left(\frac{80}{100}\right) \times \left(\frac{85}{100}\right) \]\[ \text{SP} = \text{MP} \times 0.80 \times 0.85 \]\[ \text{SP} = \text{MP} \times 0.68 \]
We are given \( \text{SP} = \text{₹}571.20 \).
\[ 571.20 = \text{MP} \times 0.68 \]
\[ \text{MP} = \frac{571.20}{0.68} \]\[ \text{MP} = \text{₹}840 \]
If no discount was given, the selling price would be equal to the marked price, i.e., \( \text{SP}_{\text{no discount}} = \text{₹}840 \).
In this scenario, the shopkeeper would have earned a profit of 12%.
Let the cost price be \( \text{CP} \).
\[ \text{SP}_{\text{no discount}} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]\[ 840 = \text{CP} \times \left(1 + \frac{12}{100}\right) \]\[ 840 = \text{CP} \times \left(\frac{112}{100}\right) \]\[ 840 = \text{CP} \times 1.12 \]
\[ \text{CP} = \frac{840}{1.12} \]\[ \text{CP} = \text{₹}750 \]
C) The cost price of the item is ₹750.
The question asks to identify which Act Jawaharlal Nehru famously described as a "new charter of slavery." This requires knowledge of key statements made by prominent Indian leaders regarding significant legislative acts passed during the British Raj.
Correct Option: C) The Government of India Act, 1935. Jawaharlal Nehru famously called the Government of India Act, 1935, a "new charter of slavery" due to its restrictive nature and the continued British control it entailed, despite introducing some provincial autonomy.
The question asks to identify the company that launched India's first hydrogen fuel cell-powered electric car in March 2022. This is a factual question related to current affairs and automotive industry developments in India.
C) Toyota Kirloskar Motor Private Limited
Toyota Kirloskar Motor Private Limited officially launched the Toyota Mirai, India's first hydrogen fuel cell electric vehicle (FCEV), in March 2022. This was part of a pilot project to study and evaluate the car's performance on Indian roads and climatic conditions. The launch was a significant step towards promoting green mobility in India.
This problem involves work and time. We are given the relative efficiencies of two individuals, Aam and Binni, and the time they take to complete a work together. We need to find the time Aam alone takes to complete the work. We can solve this by expressing their individual work rates and then combining them.
Correct Option: C) 15 hrs
The question asks to identify the term for the numerous smaller channels a river splits into in its lower course before entering the sea. This is a common geomorphological feature related to river systems.
Correct Option: C) distributaries — Distributaries are streams that branch off and flow away from a main river, especially in a delta region, carrying water and sediment to the sea. This perfectly matches the description in the question.
This problem involves the empirical relationship between the mean, median, and mode for a moderately skewed distribution. The relationship states that Mode \(\approx\) 3 Median - 2 Mean. We are given the difference between the mode and the mean, and we need to find the difference between the mode and the median.
Recall the empirical formula relating mean, median, and mode for a moderately skewed distribution:
\[\text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean}\]Rearrange the formula to express the relationship in terms of differences. We want to find the difference between Mode and Median, so let's try to isolate terms involving Mode and Median.
From the formula, we can write:
\[\text{Mode} - \text{Median} \approx 2 \times \text{Median} - 2 \times \text{Mean}\] \[\text{Mode} - \text{Median} \approx 2 (\text{Median} - \text{Mean})\]This form is useful, but we are given the difference between Mode and Mean. Let's try another rearrangement:
\[\text{Mode} - \text{Mean} \approx 3 \times \text{Median} - 2 \times \text{Mean} - \text{Mean}\] \[\text{Mode} - \text{Mean} \approx 3 \times \text{Median} - 3 \times \text{Mean}\] \[\text{Mode} - \text{Mean} \approx 3 (\text{Median} - \text{Mean})\]This is also not directly what we need. Let's try to express \(\text{Median}\) in terms of \(\text{Mode}\) and \(\text{Mean}\) from the original formula:
\[3 \times \text{Median} \approx \text{Mode} + 2 \times \text{Mean}\] \[\text{Median} \approx \frac{\text{Mode} + 2 \times \text{Mean}}{3}\]Now, substitute this expression for \(\text{Median}\) into the difference we want to find, which is \(\text{Mode} - \text{Median}\):
\[\text{Mode} - \text{Median} \approx \text{Mode} - \left(\frac{\text{Mode} + 2 \times \text{Mean}}{3}\right)\] \[\text{Mode} - \text{Median} \approx \frac{3 \times \text{Mode} - (\text{Mode} + 2 \times \text{Mean})}{3}\] \[\text{Mode} - \text{Median} \approx \frac{3 \times \text{Mode} - \text{Mode} - 2 \times \text{Mean}}{3}\] \[\text{Mode} - \text{Median} \approx \frac{2 \times \text{Mode} - 2 \times \text{Mean}}{3}\] \[\text{Mode} - \text{Median} \approx \frac{2}{3} (\text{Mode} - \text{Mean})\]We are given that the mode exceeds its mean by 16.2, which means:
\[\text{Mode} - \text{Mean} = 16.2\]Substitute this value into the derived relationship:
\[\text{Mode} - \text{Median} \approx \frac{2}{3} (16.2)\] \[\text{Mode} - \text{Median} \approx 2 \times \frac{16.2}{3}\] \[\text{Mode} - \text{Median} \approx 2 \times 5.4\] \[\text{Mode} - \text{Median} \approx 10.8\]Thus, the mode exceeds the median by 10.8.
The question describes a situation where an individual is denied promotion based on their gender. We need to identify which Fundamental Right enshrined in the Indian Constitution addresses discrimination of this nature.
Correct Option: B) Right to Equality
The Right to Equality (Articles 14-18) guarantees equality before the law, prohibits discrimination on various grounds including sex, and ensures equality of opportunity in public employment. Denying promotion to a woman officer solely because of her gender is a clear violation of Article 16 (Equality of opportunity in matters of public employment) and Article 15 (Prohibition of discrimination on grounds of religion, race, caste, sex or place of birth), both of which fall under the Right to Equality.
If the simple interest on a certain sum for 8 years is \( \frac{11}{25} \) of the sum, then the rate of interest per annum is:
7\( \frac{1}{2} \)%
6\( \frac{1}{2} \)%
8\( \frac{1}{2} \)%
5\( \frac{1}{2} \)%
To find the rate of interest, we will use the simple interest formula: \[\text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}\]. We are given the relationship between simple interest and the principal, and the time period. We can then rearrange the formula to solve for the rate.
We can cancel \(P\) from both sides (assuming \(P \neq 0\)):
\[ \frac{11}{25} = \frac{R \times 8}{100} \]Multiply both sides by 100:
\[ \frac{11}{25} \times 100 = R \times 8 \] \[ 11 \times 4 = R \times 8 \] \[ 44 = 8R \]Divide by 8:
\[ R = \frac{44}{8} \] \[ R = \frac{11}{2} \] \[ R = 5.5 \% \]Correct Option: D) 5\( \frac{1}{2} \)%
The question asks to identify the Indian shooter who won an individual silver medal in the women's 10m air pistol event at the ISSF World Cup 2022. This requires knowledge of specific sports achievements in that year.
Correct Option: B) Esha Singh won the individual silver medal in the women's 10m air pistol event at the ISSF World Cup 2022 held in Cairo, Egypt.
To solve this problem, we need to compare the original position of each letter in the given word with its position after arranging all the letters in alphabetical order. We will count how many letters retain their original position.
| Original Position | Original Letter | Alphabetical Letter |
|---|---|---|
| 1 | D | A |
| 2 | U | C |
| 3 | P | D |
| 4 | L | E |
| 5 | I | I |
| 6 | C | L |
| 7 | A | P |
| 8 | T | T |
| 9 | E | U |
D) 2