Two pipes, when working one at a time can fill a cistern in 2 hours and 3 hours, respectively while a third pipe can drain the cistern empty in 6 hours. All the three pipes were opened together when the cistern was \( \frac{1}{6} \) full. How long will it take for the cistern to be completely full?
1 hour
1 hour 20 minutes
1 hour 30 minutes
1 hour 15 minutes
To solve this problem, we need to determine the combined rate of work of all three pipes. We'll calculate the individual rates of filling and draining, then find the net rate when all pipes are open. Finally, we'll use this net rate to find the time required to fill the remaining portion of the cistern.
D) 1 hour 15 minutes
To solve this problem, we first need to determine the cost price (CP) of the item using the given selling price (SP) and loss percentage. Once the CP is known, we can calculate the desired selling price (DSP) to achieve a 10% profit. Finally, we find the difference between the desired selling price and the original selling price to determine how much the price should have been raised.
Calculate the Cost Price (CP):
Given, Selling Price (\(SP\)) = ₹220
Loss = 12%
The formula for selling price with a loss is:
\[ SP = CP \times \left(1 - \frac{\text{Loss%}}{100}\right) \]Substitute the given values:
\[ 220 = CP \times \left(1 - \frac{12}{100}\right) \] \[ 220 = CP \times \left(\frac{100 - 12}{100}\right) \] \[ 220 = CP \times \frac{88}{100} \]Now, solve for CP:
\[ CP = \frac{220 \times 100}{88} \] \[ CP = \frac{22000}{88} \] \[ CP = 250 \text{ (₹)} \]So, the Cost Price of the item is ₹250.
Calculate the Desired Selling Price (DSP) for a 10% profit:
Desired Profit = 10%
The formula for selling price with a profit is:
\[ DSP = CP \times \left(1 + \frac{\text{Profit%}}{100}\right) \]Substitute the CP and desired profit percentage:
\[ DSP = 250 \times \left(1 + \frac{10}{100}\right) \] \[ DSP = 250 \times \left(\frac{100 + 10}{100}\right) \] \[ DSP = 250 \times \frac{110}{100} \] \[ DSP = 250 \times 1.1 \] \[ DSP = 275 \text{ (₹)} \]So, to make a profit of 10%, the item should have been sold for ₹275.
Calculate the amount by which the price should have been raised:
Amount to be raised = Desired Selling Price (DSP) - Original Selling Price (SP)
\[ \text{Amount} = 275 - 220 \] \[ \text{Amount} = 55 \text{ (₹)} \]Therefore, she should have raised the price by ₹55.
Correct Option: B) ₹55
To subtract decimals, align the decimal points of the numbers and then perform subtraction as with whole numbers. If one number has fewer decimal places than the other, you can add trailing zeros to make the number of decimal places equal, which helps in proper alignment and calculation.
1.004
- 0.400
------- 1.004
- 0.400
-------
0.604Thus, \(1.004 - 0.4 = 0.604\).
Correct Option: A) 0.604
Which of the following solutions is alkaline?
[H+] = 1 × 10-4 Mol/l
[H+] < 1 × 10-7 Mol/l
[H+] > 1 × 10-7 Mol/l
[H+] = 1 × 10-7 Mol/l
To determine if a solution is alkaline, acidic, or neutral, we need to understand the relationship between the hydrogen ion concentration ([H+]) and the pH scale. A solution's acidity or alkalinity is directly related to its hydrogen ion concentration.
Correct Option: B) [H+] < 1 × 10-7 Mol/l
This condition signifies that the hydrogen ion concentration is less than that of a neutral solution. When \( [\text{H}^{+}] \) is less than \( 1 \times 10^{-7} \text{ Mol/l} \), the pH will be greater than 7, indicating an alkaline solution.
If three groups could be formed using the given figures only once, these groups would be _____.
(1,8,7), (2,6,9) and (4,3,5)
(2,5,7), (1,6,9) and (4,3,8)
(1,5,7), (2,6,8) and (4,3,9)
(1,5,7), (2,6,9) and (4,3,8)
The task is to form groups using the figures, ensuring that each group contains similar types of figures. The figures are categorized by their shapes and patterns.
Correct Option: D) (1,5,7), (2,6,9) and (4,3,8)
In the below Venn diagram which number space represents the girls who are athletes but not disciplined?
To solve this question, we need to identify the region in the Venn diagram that represents girls who are athletes but not disciplined. The diagram uses different shapes to denote categories: triangle for girls, circle for athletics, and rectangle for disciplined individuals.
Correct Option: A) 4
Choose the correct water image of the given problem figure from the answer figures.
Problem Figure
Answer Figure
To solve this problem, we need to identify the water image of the given problem figure. A water image is a reflection across a horizontal axis, which means flipping the figure upside down.
Correct Option: C) The shapes are correctly positioned above the horizontal line, and the arrow direction is reversed.
The question asks which plant hormone can be used to control dwarfism in plants. This requires knowledge of the functions of various plant growth regulators (phytohormones).
Correct Option: B) Gibberellic acid is a plant hormone that promotes stem elongation, seed germination, and flowering. It is particularly effective in reversing dwarfism in genetically dwarf plants by stimulating internode elongation.
This question asks us to identify implicit assumptions based on a given argument. An assumption is something taken for granted or supposed in advance. We need to determine which of the provided statements must be true for the argument to hold.
C) Only assumption 2 is implicit. The severe punishment of hanging rapists till death is logically based on the assumption that such a deterrent will lead to a reduction in the number of rape cases. Without this assumption, the punitive measure loses its primary societal objective.
The question asks for the definition of a physical quantity that describes the rate of change of velocity. We need to recall the fundamental definitions of the given options in physics.
Correct Option: A) Acceleration is defined as the rate of change of velocity. It measures how quickly an object's velocity changes over time.