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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%.