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Life Lesson from My Parents Applied in School Mathematics -- Try to Cover Some Extra Miles

 Try to Cover Some Extra Miles.

This photo is of my mother leading us to the top of Brahmagiri mountain when she was around 70 years old. We had been to Trambakeshwar to visit the Lord Shiva temple, one of the twelve Jyotirlingas in India. We did all the expected things like darshan-puja in the temple, taking bath in Kushavart, trekking to the Ganga Dwar etc. Our visit to Trambakeshwar could have been considered complete. 

But we came to know that the originating point of Godavari River is on the top of other side of Brahmagiri mountain. People normally visit Ganga Dwar as originating point of Godavari River which is on the city side of Brahmagiri mountain. Trekking to the top of the mountain and going on the other side to visit the actual originating point is tough, so visiting city side Ganga Dwar is considered to be equivalent to visiting the origin of Godavari River. My mother decided to do that extra mile and visit the other side of the mountain. 

It was physically too tiring for us. But the entire trek was so refreshing for the mind that we remember that visit for this extra that we did. There were few more temples related to lord Shiva and some interesting stories about river Ganga. This extra mile turned out to be the most fascinating part of the journey.

Try to cover some extra miles. This applies in every walk of life. It provides much more pleasure and learning than the main journey. Let us apply it in solving school level Mathematics questions and see the difference it makes.

I am taking an example in which concept of percentage is required. This is not a textbook question but has been taken from a real-life situation.

'A readymade garment shop is having two promo schemes:

A) Buy 2 get 2 free. You need to pay for the two highest priced items of the 4 items selected by you under this offer.

B) Flat 40% off.

You select 4 shirts for purchase. They are priced at ₹2000, ₹3000, ₹3500 and ₹1500 respectively. Which offer is better for you?'

It's easy. You can check the amount you have to pay under these offers and the one in which you have to pay less is better. Of course, the discount you get in that offer is better than the other one. In the Option A, you have to pay for the highest priced 2 items among the 4 you have selected. So, you pay for the shirts priced at ₹3500 and ₹3000. You pay ₹6500 and get the two other shirts free. Total price of the 4 shirts you got is sum of their prices which is ₹10000.

In Option B, you get 40% discount. Total price of the 4 shirts selected by you is ₹10000. You get 40% of this as discount which is ₹4000. So, you pay ₹6000 only to get the 4 shirts. In this case, Option B is better because Option A requires you to pay ₹6500 for the same shirts which is ₹500 more than what you pay in Option B. 

In solving this question, one observes few interesting points. One is that the discount in Option A is not 50% as it may seem to be. It depends on the price of items selected. With the shirts selected in this question, the effective discount is only 35% as one has to pay ₹6500 for 4 shirts having total price of ₹10000. At this stage one can feel satisfied with all these learnings.

Let us do some extra miles. Can you replace the ₹3500 shirt with some other shirt so that Option A becomes better? What should be the price of this shirt? As you change the price, how does the % discount change in Option A? What is the maximum discount possible in terms of % in Option A and for that what condition should be met? If you have to change one shirt to get maximum discount in terms of %, which shirt would you change? 

Just try thinking about these questions and observe how deep it takes you into the concept of percentage.

Covering extra miles is not equivalent to solving some more questions. You may solve many independent questions one after other, still you may not get to the nuances of the topic that these extra miles make you understand.

We are helping students apply such strategies through our online courses here. Learning various subjects with right strategy can help students succeed in tough competitive examinations without any extra coaching. Anyone needing any help in this regard can directly contact me without any hesitation.