This is a straightforward Question Answer type discussion focused on one problem related to fitness planning and some variations to it that takes deep into the concept of average and exposes some of the errors people make while using it. Question: Rohan is on a fitness drive. He has planned to burn 300 kcal in one exercise session is Gym. He has been suggested to do warmup, cardio, strength training and cooling. He divided his target kcal into 4 equal parts of 75 kcal each. His fitness tracker displays few data including calorie burnt.  Warmup burns 4 calories per minute, cardio exercise burns 8 kcal per minute, strength exercises 10 kcal per minute and cooling 2 kcal per minute.  How much time he would take in the gym to complete his exercise.  Answer: Since Rohan wants to burn 75 kcal in each of the four parts , calculate the time for each activity separately. Warm-up: Burns 4 kcal/min Time = 75 ÷ 4 = 18.75 minutes (18 min 45 sec) Cardio: Burns 8 kcal/min Time = 75 ÷...

 This quiz takes you through four common situations which most of the students come across while learning. It also has four options in each of the situations. You will find them familiar. Click on the options to see the feedback.  Once you go through all the four questions, you can end the quiz and reflect on your learning strategy. Quiz: How Effective Is Your Learning Strategy? Getting the correct answer is important—but how you learn may matter even more. Imagine yourself in each of the following situations and choose the option you think is the most effective way to learn, not just the easiest or fastest. There are no marks. The purpose is to reflect on your learning habits. Start Quiz Question 1 of 4 Question text goes here? Try Again Next Question Your Core Reflection Want to explore these ideas further? Read our article on the Five Elements of Effective Lea...

  Some mathematical problems are beautiful not because of their answer, but because they can be approached in more than one way. The following puzzle is one such example. One method leads us through the fascinating world of infinite geometric series, while another arrives at the same answer through a simple observation. Exploring both approaches reminds us that mathematics is not just about reaching the destination—it is also about appreciating the different paths that lead there. Two trains are 100 km apart and moving toward each other, each at 50 km/h. A bird starts from the front of one train and flies toward the other at 100 km/h. When it reaches the second train, it instantly turns around and flies back toward the first train. It continues flying back and forth until the trains collide. How far does the bird fly? Many people try to calculate the distance of each individual trip, creating an infinite series. But this problem can be solved instantly by understanding it thoroughl...

  A Classroom Episode The bell had just rung when Mr. Sharma walked into the classroom with a strange smile. He asked a question. Imagine we have 100 kg of fresh mushrooms. These mushrooms are 99% water. We leave them out in the sun for a day. The next morning, they are 98% water. What do you think their new weight is?” A few students looked at one another. Then Rahul raised his hand with confidence. “Sir, it lost 1% water. So, 1% of 100 kg is 1 kg. The new weight must be 99 kg.” Several students nodded immediately.  Dilip felt something different. Water is not 100%. It's 99%. The loss of 1% is in water content. So only 0.99 kg is lost. And new weight should be 99.01 kg. This looked more convincing. Several students including Rahul agreed on this. Mr. Sharma did not reject or accept the answer. He waited as few students were still working. They were looking enthusiastic.  Suddenly, Neha raised her hand and said, "Sir, the new weight should be 50 kg." Many students laughed...

  A student was simply solving a routine word problem of Class 10 when he noticed something strange. A tiny shortcut appeared to give the answer instantly. The class was impressed. Then someone asked the question that turns school mathematics into mathematical investigation. The Original Question : A man bought some pens for ₹5760. If each pen had cost ₹8 less, he would have received 10 more pens for the same amount. Find: The original cost of each pen The number of pens bought originally Most students solved it algebraically. Let the original cost per pen be p. Then the original number of pens is: 5760/p If the price decreases by ₹8, the new price becomes: p-8 And the new number of pens becomes: 5760/(p-8) Since he gets 10 more pens: (5760/p) +10 = 5760/(p-8) 5760 ( p − 8 ) + 10 p ( p − 8 ) = 5760 p . 5760p-46080+10p^2-80p=5760p. 10 p^ 2 − 80 p − 46080 = 0. p^ 2 − 8 p − 4608 = 0. Solving gives: p = 72 Original cost = ₹72 Original number of pens = 5760/72 = 80 At this stage, it ...