A can complete a piece of work alone in 10 days and B can complete the same piece of work alone in 15 days. Working together, A, B and C can complete this work in 4 \( \frac{1}{2} \) days. If B does not work, while A and C work on alternate days starting with A, then in how many days will the work be completed?
12 \( \frac{2}{3} \)
13 \( \frac{1}{5} \)
13
13 \( \frac{1}{9} \)
This problem involves work and time. We need to calculate the individual work rates of A, B, and C, then determine C's work rate. Finally, we'll calculate the time taken to complete the work when A and C work on alternate days.
Calculate individual work rates of A and B:
Calculate the combined work rate of A, B, and C:
Calculate C's individual work rate:
Calculate the work done by A and C on alternate days:
Determine the number of cycles to complete the work:
Calculate the time for the remaining work:
Total time taken:
A) \(12 \frac{2}{3}\)
In a certain code language, ‘SOLVE’ is coded as ‘QRJYC’ and ‘FENCE’ is coded as ‘DHLFC’. How will ‘TASTE’ be coded in that language?
The problem involves decoding a pattern in a given code language. We need to identify the rule applied to transform the original words into their coded forms and then apply the same rule to the target word.
Correct Option: C) RDQWC
To find the cost price when the selling price and profit percentage are given, we use the formula relating selling price, cost price, and profit percentage. The selling price is the cost price plus the profit. Since the profit is given as a percentage of the cost price, we can set up an equation to solve for the cost price.
The selling price is the cost price plus the profit. Profit is calculated as a percentage of the cost price.
\[ \text{SP} = \text{CP} + \left( \frac{P}{100} \times \text{CP} \right) \]Thus, the cost price of the sewing machine is Rs 18,000.
C) Rs 18,000.00 is the correct cost price calculated using the given selling price and profit percentage.
The question asks to identify the specific Article in the Indian Constitution that declares Hindi in Devanagari script as the official language of the Union. This requires knowledge of the constitutional provisions related to official languages.
Correct Option: D) Article 343
Article 343(1) of the Indian Constitution clearly states that "The official language of the Union shall be Hindi in Devanagari script." This article lays down the fundamental provision regarding the official language of the central government.
The resistance of a conductor depends on its material, length, and cross-sectional area. The relationship between these parameters is given by a specific formula. We need to analyze how resistance changes when the length is altered while keeping other factors constant.
Recall the formula for resistance: The resistance \(R\) of a conductor is given by the formula:
\[ R = \rho \frac{L}{A} \]where:
Identify constant parameters: The question states that "other parameters" are kept constant. This means the resistivity \(\rho\) and the cross-sectional area \(A\) remain unchanged.
Analyze the relationship between R and L: From the formula, we can see that resistance \(R\) is directly proportional to the length \(L\) of the conductor, assuming \(\rho\) and \(A\) are constant. This can be written as:
\[ R \propto L \]Determine the effect of doubling the length: If the length \(L\) is doubled, i.e., \(L' = 2L\), and \(\rho\) and \(A\) remain constant, the new resistance \(R'\) will be:
\[ R' = \rho \frac{L'}{A} = \rho \frac{2L}{A} = 2 \left( \rho \frac{L}{A} \right) = 2R \]Thus, the new resistance \(R'\) becomes twice the original resistance \(R\).
C) doubled — As derived from the formula \(R = \rho \frac{L}{A}\), resistance is directly proportional to length. Therefore, if the length is doubled, the resistance will also double, assuming resistivity and cross-sectional area remain constant.
The question asks to identify which of the given options is NOT a function of Gram Panchayats. To answer this, we need to recall the typical functions and responsibilities assigned to Gram Panchayats under the Indian Panchayati Raj system.
Correct Option: D) Scrutinises and approves budgets of the Block Samitis
In the following table, where would a broken plastic bucket be placed?
| Safely combustible | Not safely combustible | |
| Recyclable | A | B |
| Non-recyclable | C | D |
The question asks to classify a broken plastic bucket based on its combustibility and recyclability. We need to determine if plastic is safely combustible, not safely combustible, recyclable, or non-recyclable.
B) Cell B or D. While a plastic bucket is recyclable, it is not safely combustible. Therefore, it fits into the category of "Not safely combustible" and "Recyclable", which is Cell B. If for some reason it was not recyclable (e.g., highly contaminated or mixed plastic), it would fall into Cell D (Not safely combustible, Non-recyclable). However, standard plastic buckets are generally recyclable. The option "Cell B or D" covers both scenarios where it is not safely combustible, acknowledging the variability in recyclability depending on specific conditions, but primarily pointing to B if recyclable. Given the general nature of the question, plastic is not safely combustible, and many plastics are recyclable, making B the primary fit. The inclusion of D suggests considering cases where recycling might not be feasible, but the unsafe combustibility remains constant.
Vaishnavi starts walking towards the south. She walks 10 m, turns right and walks 5 m. She then turns right and walks for 3 m. Next, she again turns right and walks 10 m. Again, she takes a right and walks 8 m. Finally, she again turns right and walks 6 m.
In which direction is she facing now? (All turns are 90° turns only.)
To determine the final direction Vaishnavi is facing, we need to track her orientation after each turn. We can visualize this by imagining a person walking and turning, or by using a compass direction system (North, South, East, West).
The distances walked (10 m, 5 m, 3 m, 10 m, 8 m, 6 m) are irrelevant for determining the direction she is facing; they would only be needed if the question asked for her final position relative to the starting point.
Therefore, after all the turns, Vaishnavi is facing West.
B) West
The question asks for the definition of the 'multiplier' in economics, specifically the ratio of increase in income to increase in what. Understanding the concept of the Keynesian multiplier is key here.
Correct Option: D) investment
The multiplier in economics, especially the investment multiplier, measures the impact of a change in investment on the overall national income. An initial increase in investment leads to a chain reaction of spending and re-spending, resulting in a larger increase in total income.
A solid right cylinder having a base diameter of 10 cm and height 2 cm is melted and recast into right cylindrical coins with a base diameter of 1 cm and a thickness of 0.2 cm. Find the number of coins that can be made.
When a solid object is melted and recast into smaller objects, the total volume of the material remains constant. Therefore, the total volume of the large cylinder will be equal to the sum of the volumes of all the smaller coins. We can find the number of coins by dividing the volume of the large cylinder by the volume of a single coin.
Thus, 1000 coins can be made.
Correct Option: A) 1000