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Vasant can do a piece of work in 24 days. He works at it alone for 4 days and his friend Ritu alone finishes the remaining work in 25 days. Both of them together can complete the work in:
Let's solve this step by step. First, let's find out how much work Vasant can complete in one day. Since Vasant can do the entire piece of work in 24 days, his work rate is: \[ \text{Vasant's work rate} = \frac{1}{24} \text{ (work per day)} \] Vasant works alone for 4 days, so the fraction of the woRead more
Let’s solve this step by step.
First, let’s find out how much work Vasant can complete in one day. Since Vasant can do the entire piece of work in 24 days, his work rate is:
\[
\text{Vasant’s work rate} = \frac{1}{24} \text{ (work per day)}
\]
Vasant works alone for 4 days, so the fraction of the work he completes is:
\[
\text{Work done by Vasant} = 4 \times \frac{1}{24} = \frac{1}{6}
\]
This means that after Vasant works for 4 days, \(\frac{1}{6}\) of the work is done and \(\frac{5}{6}\) of the work is remaining.
Ritu completes the remaining \(\frac{5}{6}\) of the work in 25 days. So, Ritu’s work rate is:
\[
\text{Ritu’s work rate} = \frac{\frac{5}{6}}{25} = \frac{1}{30} \text{ (work per day)}
\]
Now, we want to find out how long it would take for Vasant and Ritu to complete the work together. The combined work rate of Vasant and Ritu is:
\[
\text{Combined work rate} = \text{Vasant’s work rate} + \text{Ritu’s work rate} = \frac{1}{24} + \frac{1}{30}
\]
To find the time taken for them to complete the work together, we take the reciprocal of their combined work rate:
\[
\text{Time taken together} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{1}{24} + \frac{1}{30}}
\]
Let’s calculate the exact value of the time taken together using this formula.
The time taken for Vasant and Ritu to complete the work together is:
\[
\text{Time taken together} = \frac{1}{\frac{1}{24} + \frac{1}{30}} = \frac{1}{\frac{30 + 24}{24 \times 30}} = \frac{24 \times 30}{54} = \frac{720}{54} = \frac{40}{3} = 13\frac{1}{3} \text{ days}
\]
So, Vasant and Ritu together can complete the work in \(13\frac{1}{3}\) days.
See lessAbhishek Jain typed 50 pages at the rate of 30 pages per hour on Sunday. On Monday, he could only type 50 extra pages at the rate of 20 pages per hour. What has his average rate of typing been overall. Calculate in pages per hour?
To find Abhishek Jain's average typing rate overall, we can use the formula: \[ \text{Average Rate} = \frac{\text{Total Pages Typed}}{\text{Total Time Spent Typing}} \] On Sunday, he typed 50 pages at the rate of 30 pages per hour. So, the time spent typing on Sunday is: \[ \text{Time on Sunday} = \Read more
To find Abhishek Jain’s average typing rate overall, we can use the formula:
\[
\text{Average Rate} = \frac{\text{Total Pages Typed}}{\text{Total Time Spent Typing}}
\]
On Sunday, he typed 50 pages at the rate of 30 pages per hour. So, the time spent typing on Sunday is:
\[
\text{Time on Sunday} = \frac{\text{Pages Typed}}{\text{Rate}} = \frac{50}{30} \text{ hours}
\]
On Monday, he typed 50 extra pages at the rate of 20 pages per hour. So, the time spent typing on Monday is:
\[
\text{Time on Monday} = \frac{\text{Pages Typed}}{\text{Rate}} = \frac{50}{20} \text{ hours}
\]
The total pages typed over both days is:
\[
\text{Total Pages Typed} = 50 + 50 = 100 \text{ pages}
\]
The total time spent typing is:
\[
\text{Total Time Spent Typing} = \text{Time on Sunday} + \text{Time on Monday} = \frac{50}{30} + \frac{50}{20} \text{ hours}
\]
Now, we can calculate the average rate:
\[
\text{Average Rate} = \frac{\text{Total Pages Typed}}{\text{Total Time Spent Typing}} = \frac{100}{\frac{50}{30} + \frac{50}{20}} \text{ pages per hour}
\]
\[
\text{Average Rate} = \frac{100}{\frac{5}{3} + \frac{5}{2}} = \frac{100}{\frac{10}{6} + \frac{15}{6}} = \frac{100}{\frac{25}{6}} = \frac{100 \times 6}{25} = \frac{600}{25} = 24 \text{ pages per hour}
\]
So, Abhishek Jain’s average typing rate overall is 24 pages per hour.
See lessMr. Sinha distributes a certain sum of money among his five sons, one daughter and his wife in such a way that each son gets double the amount of his daughter and the wife gets double the amount of each son. If each son gets Rs. 15000, what was the total amount distributed?
Let's assume the amount received by the daughter is \(x\). According to the problem, each son gets double the amount of the daughter, so each son gets \(2x\). It is given that each son receives Rs. 15,000, so we can set up the equation: \[2x = 15,000\] Solving for \(x\), we get: \[x = \frac{15,000}{Read more
Let’s assume the amount received by the daughter is \(x\). According to the problem, each son gets double the amount of the daughter, so each son gets \(2x\). It is given that each son receives Rs. 15,000, so we can set up the equation:
\[2x = 15,000\]
Solving for \(x\), we get:
\[x = \frac{15,000}{2} = 7,500\]
So, the daughter receives Rs. 7,500.
The wife receives double the amount of each son, which is:
\[2 \times 15,000 = 30,000\]
Now, the total amount distributed is the sum of the amounts received by all family members:
\[5 \times (\text{amount received by each son}) + \text{amount received by the daughter} + \text{amount received by the wife}\]
\[= 5 \times 15,000 + 7,500 + 30,000 = 75,000 + 7,500 + 30,000 = 112,500\]
Therefore, the total amount distributed by Mr. Sinha is Rs. 112,500.
See lessWhich of the following statements are true? Justify your answers. This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. The total number of all possible samples of size 3 without replacement from a population of size 7 is 21 .
To evaluate the statement "The total number of all possible samples of size 3 without replacement from a population of size 7 is 21," we need to use the concept of combinations. Combination Formula The number of ways to choose a sample of size \(r\) from a population of size \(n\) without replacemenRead more
To evaluate the statement “The total number of all possible samples of size 3 without replacement from a population of size 7 is 21,” we need to use the concept of combinations.
Combination Formula
The number of ways to choose a sample of size \(r\) from a population of size \(n\) without replacement is given by the combination formula:
\[
C(n, r) = \frac{n!}{r!(n-r)!}
\]
where \(n!\) denotes the factorial of \(n\).
Application to the Statement
In this case, we have a population size \(n = 7\) and a sample size \(r = 3\). Plugging these values into the combination formula:
\[
C(7, 3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3! \times 4!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35
\]
Conclusion
The statement “The total number of all possible samples of size 3 without replacement from a population of size 7 is 21” is false. The correct number of samples is 35.
See lessThe entropy change is not a good criterion for spontaneity of a thermodynamic process. Comment.
The statement "The entropy change is not a good criterion for spontaneity of a thermodynamic process" is generally true, and here's why: 1. **Definition of Spontaneity:** - A process is said to be spontaneous if it occurs without any external intervention. In thermodynamics, the spontaneity of a proRead more
The statement “The entropy change is not a good criterion for spontaneity of a thermodynamic process” is generally true, and here’s why:
1. **Definition of Spontaneity:**
– A process is said to be spontaneous if it occurs without any external intervention. In thermodynamics, the spontaneity of a process is determined by the change in Gibbs free energy (\(ΔG\)), not just by the change in entropy (\(ΔS\)).
2. **Role of Entropy:**
– Entropy (\(S\)) is a measure of disorder or randomness in a system. While an increase in entropy (\(ΔS > 0\)) is a factor that favors spontaneity, it is not the sole determinant. A process can have a positive entropy change and still be non-spontaneous under certain conditions.
3. **Gibbs Free Energy:**
See less– The Gibbs free energy (\(ΔG\)) is a more comprehensive criterion for spontaneity, as it takes into account both the entropy change (\(ΔS\)) and the enthalpy change (\(ΔH\)) of a process, as well as the temperature (\(T\)):
\[ΔG = ΔH – TΔS\]
– A process is spontaneous at a given temperature if \(ΔG < 0\). This criterion incorporates the effects of both entropy and enthalpy changes. 4. **Temperature Dependence:** - The spontaneity of a process can also depend on temperature. A process that is non-spontaneous at one temperature might become spontaneous at a different temperature. This is because the \(TΔS\) term in the Gibbs free energy equation can become more significant at higher temperatures. ### **Conclusion:** While entropy change is an important factor in determining the spontaneity of a thermodynamic process, it is not a standalone criterion. The Gibbs free energy change (\(ΔG\)) is a more reliable indicator of spontaneity, as it considers both entropy and enthalpy changes, as well as the temperature of the system.
Write True (T) or False (F) against the following statements:
a) False b) True c) False d) True e) True
a) False
See lessb) True
c) False
d) True
e) True
Fill in the blanks.
a) Arm sling is done for support of Elbow Fracture. b) Frost Nip is an early stage of Frost Bite. c) The most important stretcher used in rescue operations is Scoop Stretcher. d) Chest compression and rescue breaths are given at the rate of 30:2. e) Jaw Thrust is the method to open airway in suspectRead more
a) Arm sling is done for support of Elbow Fracture.
See lessb) Frost Nip is an early stage of Frost Bite.
c) The most important stretcher used in rescue operations is Scoop Stretcher.
d) Chest compression and rescue breaths are given at the rate of 30:2.
e) Jaw Thrust is the method to open airway in suspected neck and spinal injury.
Explain the First Aid and Do’s and Don’ts in case of a victim with near drowning experience.
1. Understanding Near Drowning Near drowning occurs when someone almost suffocates from being underwater, usually in a body of water like a pool, lake, or bathtub. It's a serious situation that requires immediate action to prevent death or long-term complications. 2. First Aid for Near DrowningRead more
1. Understanding Near Drowning
Near drowning occurs when someone almost suffocates from being underwater, usually in a body of water like a pool, lake, or bathtub. It's a serious situation that requires immediate action to prevent death or long-term complications.
2. First Aid for Near Drowning Victims
The following steps can be taken to provide first aid to a near drowning victim:
a. Ensure Safety: Before approaching the victim, ensure the area is safe for you to enter. Do not put yourself at risk of drowning or injury.
b. Remove Victim from Water: If the victim is still in the water, carefully remove them as quickly as possible. Be cautious of any potential spinal injuries and try to keep the victim's head and neck stabilized.
c. Check Responsiveness: Check if the victim is responsive by gently tapping their shoulder and asking if they are okay. Look for signs of breathing or movement.
d. Open Airway and Check Breathing: If the victim is not breathing, open their airway by tilting their head back and lifting the chin. Check for breathing by listening and feeling for breaths for about 10 seconds.
e. Start CPR if Necessary: If the victim is not breathing, start CPR immediately. Give 30 chest compressions followed by two rescue breaths. Continue this cycle until help arrives or the victim starts breathing.
f. Call for Emergency Assistance: If you are alone, perform CPR for about two minutes before calling for emergency medical help. If someone is with you, have them call for help immediately.
g. Monitor Vital Signs: While waiting for help to arrive, monitor the victim's vital signs, including pulse and breathing. Be prepared to continue CPR if needed.
3. Do's and Don'ts
Do:
Don't:
4. Conclusion
Near drowning is a life-threatening emergency that requires prompt and effective action. Knowing how to recognize the signs and provide appropriate first aid can make a significant difference in the outcome for the victim. Remember to stay calm, assess the situation carefully, and provide the necessary assistance until professional help arrives.
See lessDefine Drowning.
Drowning is a form of suffocation that occurs when a person is submerged or immersed in water, leading to respiratory impairment. It can be fatal or non-fatal and typically results from water entering the lungs. Drowning deprives the body of oxygen, leading to asphyxia and eventual death if not rescRead more
Drowning is a form of suffocation that occurs when a person is submerged or immersed in water, leading to respiratory impairment. It can be fatal or non-fatal and typically results from water entering the lungs. Drowning deprives the body of oxygen, leading to asphyxia and eventual death if not rescued and resuscitated promptly.
See lessEnumerate the various Personal Protective Equipments.
Personal Protective Equipment (PPE) refers to protective clothing, helmets, goggles, or other garments or equipment designed to protect the wearer's body from injury or infection. Here are several types of PPE commonly used in various settings: Gloves: Used to protect hands from contamination oRead more
Personal Protective Equipment (PPE) refers to protective clothing, helmets, goggles, or other garments or equipment designed to protect the wearer's body from injury or infection. Here are several types of PPE commonly used in various settings:
Gloves:
Masks:
Face Shields and Goggles:
Gowns and Aprons:
Helmets:
Safety Shoes:
Ear Protection:
Respirators:
Full Body Suits:
Harnesses and Fall Protection:
It's important to use PPE correctly and according to the manufacturer's instructions to ensure maximum protection.
See less