tecscholar

Pipe and Tank Problem - Step-by-Step Solution Pipe and Tank Problem Problem: Two pipes A and B can fill a tank in 48 minutes and 66 minutes, respectively. If both pipes are opened simultaneously, after how many minutes should Pipe B be closed so that the tank gets filled in exactly 32 minutes? Step-by-Step Solution: Step 1: Calculate the rate of filling for each pipe. Pipe A fills the tank in 48 minutes, so its rate = 1/48 (portion of the tank per minute). Pipe B fills the tank in 66 minutes, so its rate = 1/66 (portion of the tank per minute). Step 2: Work done by Pipe A in 32 minutes. Since Pipe A works for the full 32 minutes, the work done by A = 32 × 1/48 = 2/3 (portion of the tank). Step 3: Determine the remaining portion of the tank to be filled. Total work to...

How Many Apples Did Naman Originally Buy? Solution Let the original price per apple be x and the number of apples bought initially be n . Step 1: Initially, the number of apples is: n = 720 / x Step 2: After the price reduction, the new price is (x - 2) , and the number of apples becomes: n + 4 = 720 / (x - 2) Step 3: Substitute n = 720 / x into the second equation: (720 / x) + 4 = 720 / (x - 2) Step 4: Simplify the equation: 720 / (x - 2) - 720 / x = 4 (720 * 2) / [x(x - 2)] = 4 1440 / [x(x - 2)] = 4 Step 5: Multiply through by x(x - 2) : 1440 = 4x(x - 2) Step 6: Simplify the quadratic equation: 1440 = 4x² - 8x x² - 2x - 360 = 0 Step 7: Solve for x by factorization: (x - 20)(x + 18) = 0 x = 20 (as price m...

Solving the Rice Price Problem Alok is looking to buy rice, and with a 24% reduction in price, he can buy 10 kg more rice for ₹2,500. Let's solve the problem and find out the reduced rate of rice per kg. Step 1: Defining Variables Let the original price of rice per kg be ₹x. After a 24% reduction, the new price per kg is 76% of the original price, which is 0.76x . Step 2: Setting Up the Equation At the original price, Alok can buy: Quantity at original price = 2500 / x At the reduced price, Alok can buy: Quantity at reduced price = 2500 / (0.76x) The difference in the quantity of rice he can buy is 10 kg, so we have the equation: (2500 / (0.76x)) - (2500 / x) = 10 Step 3: Simplifying the Equation Factor out 2500 from the equation: 2500 * (1 / (0.76x) - 1 / x) = 10 Now, simplify the expression inside the parentheses: (1 ...

Problem Statement: If a + b + c = 6 and a² + b² + c² = 14, find the value of (a-b)² + (b-c)² + (c-a)². Solution: The formula for (a-b)² + (b-c)² + (c-a)² is: (a-b)² + (b-c)² + (c-a)² = 2(a² + b² + c²) - 2(ab + bc + ca). From the problem: a + b + c = 6 → (a + b + c)² = 36. Expand (a + b + c)²: a² + b² + c² + 2(ab + bc + ca) = 36. Substitute a² + b² + c² = 14: 14 + 2(ab + bc + ca) = 36. 2(ab + bc + ca) = 22 → ab + bc + ca = 11. Now substitute values into the formula: (a-b)² + (b-c)² + (c-a)² = 2(a² + b² + c²) - 2(ab + bc + ca). = 2(14) - 2(11) = 28 - 22 = 6. Final Answer: The value is 6 .

Election Problem Solution By TecScholar Let's solve a problem step by step where an election result is analyzed based on given conditions. Problem In an election, 2% of registered voters did not participate, and 500 votes were invalid. Candidates A and B contested the election, and A defeated B by 200 votes. If 43% of registered voters voted for A, find the total number of votes cast. Solution Let the total number of registered voters = x . Voters who participated = 98% of x , i.e., 0.98x . Invalid votes = 500 . Therefore, valid votes = 0.98x - 500 . Candidate A defeated B by 200 votes. Thus, A's votes = B's votes + 200 . 43% of registered voters voted for A. Hence, A's votes = 0.43x . Equations: Total valid votes: A's votes + B's votes = 0.98x - 500 ...

Solving the Equation: 8^x + 2^x = 130 Solving the Equation: 8 x + 2 x = 130 We are tasked with solving the equation: 8 x + 2 x = 130 We begin by expressing 8 x as a power of 2. Since 8 = 2 3 , we can rewrite the equation as: (2 3 ) x + 2 x = 130 This simplifies to: 2 3x + 2 x = 130 Let y = 2 x . Then, the equation becomes: y 3 + y = 130 Now, we need to solve the cubic equation: y 3 + y - 130 = 0 We can try some values for y to find a root. If we substitute y = 5 , we get: 5 3 + 5 = 125 + 5 = 130 So, y = 5 is a solution. Since y = 2 x , we now have: ...

Integration of x^2024 - 1 / x^506 - 1 Solving the Integral: ∫ (x^2024 - 1) / (x^506 - 1) dx The integral we are solving is: ∫ (x^2024 - 1) / (x^506 - 1) dx We start by simplifying the expression using polynomial division. Dividing x 2024 - 1 by x 506 - 1 gives: x 2024 - 1 = (x 506 - 1) * (x 1518 + x 1012 + x 506 + 1) This allows us to rewrite the integral as: ∫ (x 1518 + x 1012 + x 506 + 1) dx Now, we can integrate each term: ∫ x 1518 dx = x 1519 / 1519 ∫ x 1012 dx = x 1013 / 1013 ∫ x 506 dx = x 507 / 507 ∫ 1 dx = x Thus, the final result is: x 1519 / 1519 + x 1013 / 1013 + x 507 / 507 + x + C Where C is the constant of inte...

Question Alloy Let the weight of the initial alloy be x , with p% silver by weight. For the first condition: (px + 100 * 3) / (x + 3) = 90 90(x + 3) = px + 300 90x + 270 = px + 300 px = 90x - 30 p = 90 - (30 / x) For the second condition: (px + 90 * 2) / (x + 2) = 84 84(x + 2) = px + 180 84x + 168 = px + 180 px = 84x - 12 Substituting p = 90 - (30 / x) : (90 - 30 / x)x = 84x - 12 90x - 30 = 84x - 12 6x = 18 → x = 3 Answer: 3 kg.

Question matches Solution :- A team has played 40 matches, winning 30% of them. Let the total number of matches in the tournament be T , and the remaining matches be R = T - 40 . Matches won so far: 30% of 40 = 12. If they win 60% of the remaining matches: New total wins = 12 + 0.6R Given that their overall win percentage is 50%: (12 + 0.6R) / T = 0.5 Since T = 40 + R : 12 + 0.6R = 0.5(40 + R) 12 + 0.6R = 20 + 0.5R 0.1R = 8 → R = 80 Thus, T = 40 + 80 = 120 . If they win 90% of the remaining matches: Total wins = 12 + 0.9R = 12 + 0.9(80) = 12 + 72 = 84 . Answer: 84 matches.

Train Crossing Problem Solution To solve this problem, we need to calculate the speed of the train and then determine the time it will take to cross another train. 1. Finding the speed of the train: The train crosses a 400-meter bridge in 75 seconds, so its speed (V) is: V = distance / time = 400 / 75 = 5.33 m/s Now, converting the speed to kilometers per hour: V = 5.33 * (3600 / 1000) = 19.2 km/h 2. Speed of the second train: The second train's speed is given as 97.2 km/h, which is: V_second = 97.2 * (1000 / 3600) = 27 m/s 3. Combined speed of both trains: The combined speed of both trains is: V_total = 5.33 + 27 = 32.33 m/s 4. Time calculation: The total length of the two trains is 325 meters + 400 meters = 725 meters. The time (t) taken to cross each other is: t = total distance / total speed = 725 / 32.33 = 22.4 seconds Therefore, ...

Work Completion Time Problem Solution Problem Statement Rahul started a task at 9 AM. Gautam joined him two hours later, and they completed the work together at 5 PM the same day. If both had started at 9 AM, they would have finished the task 30 minutes earlier. The question is: how much time would Rahul take to complete the task alone? Step 1: Defining the Variables Let us define the following variables: Total work : 1 unit Rahul’s work rate : R (work per hour) Gautam’s work rate : G (work per hour) Step 2: Understanding the Two Scenarios Scenario 1: Rahul starts at 9 AM, and Gautam joins at 11 AM Rahul works alone from 9 AM to 11 AM, which is 2 hours. He completes 2R units of work during this time. Then, from 11 AM to 5 PM (6 hours), both work together, completing 6(R + G) units of work. Thus, the total work completed is: ...

Apple Selling Problem Apple Selling Problem A person sells 64 apples for ₹60, making a 25% profit. If they incur a 40% loss, how many apples will they sell for ₹36? Solution Find the Cost Price (CP) of 64 apples: We use the formula for profit: SP = CP × (1 + Profit% / 100) Substitute the values: 60 = CP × (1 + 25 / 100) 60 = CP × 1.25 CP = 60 / 1.25 = ₹48 Find the CP of 1 apple: The CP of 64 apples is ₹48. So, the CP of 1 apple is: 48 / 64 = ₹0.75 Find the SP of 1 apple with a 40% loss: Use the formula for loss: SP = CP × (1 - Loss% / 100) Substitute the values: SP = 0.75 × (1 - 40 / 100) SP = 0.75 × 0.6 = ₹0.45 Find the number of apples sold for ₹36: ...

Price of Petrol Increases by 19% If the Price of Petrol Increases by 19% and the Consumption Decreases by 19%, Find the Effect on the Expenses The price of petrol increases by 19%, and the consumption decreases by 19%. We need to find the effect on the total expenses. Solution: Let the initial price of petrol be P and the initial consumption be C . The initial expenses = P × C . After the increase of 19% in price, the new price is P × 1.19 . After the decrease of 19% in consumption, the new consumption is C × 0.81 . The new expenses = P × 1.19 × C × 0.81 = P × C × 0.9639 . Hence, the new expenses are 96.39% of the initial expenses . Final Answer: The total expenses decrease by 3.61% .

If Mohan Buys 20 Buttons for ₹1 If Mohan buys 20 buttons for ₹1, how many buttons should he sell for ₹1 to make a profit of 25%? Options: A) 18 B) 16 C) 15 D) 20 Solution: Cost price of 1 button = ₹1 / 20 = ₹0.05 Selling price of 1 button = ₹0.05 × 1.25 = ₹0.0625 Number of buttons sold for ₹1 = ₹1 / ₹0.0625 = 16 Mohan should sell 16 buttons for ₹1 to make a profit of 25%.

Profit and Loss Problem A person wanted to sell an article at 20% profit; But actually he sold it at Rs 480 at a 20% loss. At what price (in rupees) did he want to sell it to make profit? Solution: Given that the article was sold at a 20% loss for Rs 480, we need to find the cost price (C.P.) and the desired selling price (S.P.) for a 20% profit. Step 1: Calculate the Cost Price (C.P.) Since the article was sold at a 20% loss, use the formula: Loss = (Loss Percentage × C.P.) / 100 480 = C.P. × (80 / 100) C.P. = (480 × 100) / 80 = Rs 600 Step 2: Calculate the Desired Selling Price (S.P.) for 20% Profit Profit = (Profit Percentage × C.P.) / 100 Desired S.P. = C.P. + Profit = 600 + (20 × 600) / 100 = 600 + 120 = Rs 720 Shortcut Method: Use the formulas directly: C.P. = (480 × 100) / 80 = Rs 600 Desired S.P. = (6...

Zoo Rabbit and Pigeon Problem In a zoo, there are rabbits and pigeons. If heads are counted, there are 340 heads and if legs are counted, there are 1060 legs. How many pigeons are there? Solution: Let the number of rabbits be R, and the number of pigeons be P. Each rabbit has 1 head and 4 legs, while each pigeon has 1 head and 2 legs. We have two equations: R + P = 340 (Total heads) 4R + 2P = 1060 (Total legs) Solving these equations: From the second equation: 2R + P = 530. Subtract the first equation from the second: 2R + P - (R + P) = 530 - 340, which gives R = 190. Substitute R = 190 into the first equation: 190 + P = 340, so P = 150. Answer: There are 150 pigeons.

  Keylogger is a process of recording Keystrokes actions. When the user presses the key then the keylogger records it. Keylogger is also Known as Keystroke capturing. Keylogger is a collect private and sensitive information of user without knowing and monitor the device. Keylogger is a provide the visual surveillance to monitor device on user and track the file creation, updating copy or paste operation and record the messages and snapshots of the phone at the regular of the time.   Type of Keylogger :-   •         Hardware Keylogger •         Software Keylogger Hardware Keylogger :- Hardware Keylogger is a physical device that capture keystrokes of computers and others types of devices. Several Category of the Hardware Keylogger :- (1) External USB (2)   BIOS embedded (3)   Keyboard (4)   Acoustic   Software Keylogger :- Software Keylogger is a software pr...

Static Routing :-  Static Routing is a form of technology that occurs when routers manually configured by the without machine. Important points about the Static Routing :- Static Routing is also known as non-adaptive Routing Which means it can't modify whenever network administrator not change the ip address of the routers. Static Routing is a handle by manually or network administrator. In Static Routing network administrator is a add and define the path of routers. Static Routing is a Small scale level network. Static Routing is not a use complex algorithm. If any failure occurs in Static Routing then we can rerouting but in a dynamic routing it's not possible do this. Static Routing is a more difficult to configure as compared to the dynamic routing. Advantages of  the Static Routing :- Small Scale level network. No overhead. High Security. Not use Bandwidth in a Static Routing. Define the  default gateway. Disadvantages of the Static Routing :- Human Error. Fault tole...

Java is a High level Programming Language. Java was invented by the James Gosling. James Gosling is a known as father of the java. Java was launched by the Sun Microsystems company in a USA in a 1995 . Java was initially is a known as Oak but In a 1995 Oak was renamed Java. Syntax of Java is similar to the  C++ and C Language. Key points of Java :- Java is a Object Oriented based Programming Language. Java code is a run on a Java Virtual Machine. Java is a Secure and Robust Programming Language. Java is a both Compiled and Interpreted Programming Language. Java is a Case sensitive Programming Language. Java is not a Platform dependent and Portable Programming Language. Java is a Dynamic and Extensible Programming Language. Java is a High Performance Programming Language. Java is a Distributed Programming Language. Java is a Multithreaded and Interactive Programming Language. Java Development Kit :- Java Development Kit is a collection of tools that are used for developing ...

The Full of a HTML is a Hyper Text Markup Language. HTML is a combination of a two words one is a Hyper Text and second one is a Markup Language. Hyper Text is a give information about the link between the Web-pages. Markup Language tells about the text document within tags and Structure of a Web-Pages.  HTML [Hyper Text Markup Language] was developed by Physicist Scientists Tim Berners Lee in 1991.  HTML [Hyper Text Markup Language] is a used for to create Web-Pages and Web Application. HTML [Hyper Text Markup Language] is a create only static Web-Pages. HTML is a   [Hyper Text Markup Language]   mostly used for Web activity. HTML [Hyper Text Markup Language] is a Markup Language not a Programming Language.  The file extension of a HTML  [Hyper Text Markup Language] is a .html or .htm. History of a HTML    [Hyper Text Markup Language] :- HTML [Hyper Text Markup Language] was developed by Physicist Scientists Tim Berners Lee in 1991....