Maths Problem Using LCM

Question:

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. She says she doesn't know, but she remembers somethings from various ways she tried packing the eggs.

When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over.

What can the farmer figure from this information about the number of
eggs she had?

Answer:

Let N = total number of eggs.

N is not evenly divisible by 2, 3, 4, 5, or 6. There is always 1 left over.
N is evenly divisible by 7. There is 0 left over.

So, we want to find an N that is a multiple of 7 and a (N-1) that is a common multiple of 2, 3, 4, 5, and 6.

For 2, 3, 4, 5, and 6 the prime factors are:
2:   2
3:   3
4:   2*2
5:   5
6:   2*3
So, the LCM is 2*2*3*5 = 60.

Find the multiples of 60 and add 1 (since dividing by 2, 3, 4, 5, and 6 always has a remainder of 1).

The multiples of that LCM are:
 60  120  180  240  300  360  420  480  540

                     

Add 1:  

61  121  181  241  301  361  421  481  541
 

Remainder when divided by 7:    

 5      2     6      3      0     4      1     5      2   

The remainder of (N divided by 7) is 0 (it is evenly divisible). So, N=301.

(Note: N could also be 721, 1141, 1561, 1981, 2401, 2821, 3241, 3661, etc., but 301 is the least value. Since the remainder repeats, you can find each of these values by adding 420.) 

[Note: 420 is the LCM of 2,3,4,5,6,7]

How will India tax cryptocurrency investments?

Cryptocurrency is surging in popularity in India as an investment and, increasingly, a means of payment by companies for their products and services. This brings in the question of how to pay taxes on those types of transactions.

While the Reserve Bank of India (RBI) has not granted legal tender status to bitcoin and other cryptocurrencies, there is no escape from paying tax on cryptocurrency investment gains. The Indian government is planning to compartmentalise virtual currencies and their tax treatment on the basis of their use cases—payments, investment, or utility, according to the Economic Times.

“Cryptocurrency gains could happen from multiple ways such as mining, staking, farming, or conventional buying and selling,” said Edul Patel, co-founder and CEO of San Francisco-headquartered cryptocurrency trading platform Mudrex. Gains from trading digital assets could be categorized under ‘business income’, while other activities would likely fall under ‘income from other sources.’ Bringing in additional rules or amendments would needlessly burden the taxpayer, Patel said.

High-powered computers ‘mine’ bitcoin by solving complex mathematical puzzles that result in a bitcoin reward. Similarly, cryptocurrency staking provides a token reward for determining whether a transaction conforms to certain protocol requirements. Yield farming, which typically takes place using the ethereum ecosystem, involves lending out crypto assets in return for a payment.

While it’s not yet clear that the Indian government will set out a regulatory framework for virtual assets, it has provided some provisions for transparency.

In March, the Indian government made it mandatory for companies dealing with virtual currencies to disclose profit or loss incurred on crypto transactions and the amount of cryptocurrency they hold in their balance sheets. The amendments made in the Companies Act came into effect on April 1 this year.

The then-minister of state for finance, Anurag Singh Thakur, clarified that “the gains resulting from the transfer of cryptocurrencies/assets are subject to tax under the head of income, depending upon the nature of holding of the same.”

The important bit is to assess the nature of these investments.

Cryptocurrency can be classified as an investment asset or business income

A digital token is deemed to be a capital asset if it is purchased for investment, which means it is bound to be taxed under capital gains. These investments are categorised into long-term or short-term capital gains, depending on the holding period.

Any gains after holding a cryptocurrency for 36 months or more would be taxable as long-term capital gains, while gains accrued during a shorter period would be categorised as short-term capital gains. These gains are taxable as per the slab rates applicable to a taxpayer, while long-term capital gains are taxed at the flat rate of 20% with the benefit of indexation, according to Harsh Bhuta, partner at accounting firm Bhuta Shah & Co. Bhuta says “much clarity” is still required on how to treat the different types of gains and income.

The tax rate under the long-term category can decline once the indexation benefit is applied, which allows the investor to adjust for inflation during the period these investments were held. Every year, the Central Board of Direct Taxes releases the cost inflation on which these assessments are done.

On the other hand, if a trader carries out cryptocurrency transactions frequently, any profits thereon would be taxable as business income.

India’s cryptocurrency bill could require more disclosure

Many countries already have a taxation system for cryptocurrency gains in place, but India’s frigid response to the virtual currency ecosystem makes it tough for investors to file their tax returns. Indians had parked nearly $6.6 billion (Rs49,189 crore) in cryptocurrencies as of May this year, as compared to around just $923 million until April 2020, according to blockchain data firm Chainalysis.

As cryptocurrency regulations in India remain ambiguous, a growing number of Indians are accessing digital tokens by buying and selling on foreign platforms, which may have better features and customer service. If Indian authorities warm to the crypto token market, however, that could pull some of that business back to domestic crypto exchanges.

The Indian government may levy the 18% Goods and Services Tax (GST) on transactions on foreign cryptocurrency exchanges in order to level the playing field with domestic ones, according to reports in July. India has also reportedly considered a 2% equalisation levy on transactions with foreign crypto exchanges. For Indian cryptocurrency exchanges, the 18% GST is charged as the trading fee to customers, which is similar to the setup for stock brokerages.

Market players are now biting their nails ahead of the winter session of the Indian parliament, when the country’s first cryptocurrency legislation is likely to be presented. The Cryptocurrency and Regulation of Official Digital Currency Bill is expected to contain disclosure requirements for income tax returns for crypto holdings in India as well as on foreign crypto exchanges by Indian residents.

This may allow the government to regulate cryptocurrency transactions, and the legitimacy provided to digital tokens could give investors more confidence in the sector. Many cryptocurrency enthusiasts believe that regulating cryptocurrency will generate tax revenues for the Indian government as well. Bhuta expects the Indian government may introduce special income tax rates to tax profits from cryptocurrency transactions and may identify such transactions through recognized platforms only.

“It would be a massive source of revenue for the government, which is currently burdened with a large fiscal deficit,” Patel said. “The government realizes the importance of employment opportunities in the several new startups that have sprawled up around the crypto ecosystem. The government should likely focus on creating a robust taxation framework that is easy to understand and simple to implement.”

How to Start Investing in Crypto Currency like Bitcoin

While Bitcoin is popular, understanding the fundamentals that drive its pricing and adoption is important.

Blockchain is a distributed ledger that records transactions between two parties in a safe and open manner. Blockchain technology has revolutionized the way transactions are processed – transactions are now decentralized, scalable, operating 24x7 without a central middleman and highly secured. Bitcoin, the first application of blockchain in the real world, acts like a payment mechanism as well as a store of value.

As an investor in this asset class, it is pertinent to understand the fundamentals that drive Bitcoin (also referred as BTC in exchanges as a ticker). This article will help you to understand the brief history as well as the potential growth that cryptocurrencies can have in the upcoming years.

Supply and trade

Bitcoin has a fixed supply of 21 million out of which 18.8 million are already in circulation. Every day, about 900 BTCs are added to the supply (via a process called mining). This reduces over time and eventually in the year 2140, all BTCs will be in circulation. However, an estimated 3 to 4 million of the 18.8 million supply is locked forever (investors have lost their access to them). Thus, BTC’s fixed supply creates an artificial scarcity that will augment its pricing in the years to come provided there is strong adoption.

However, BTC is divisible up to 8 decimals. That is, you can transact/buy even 0.00000001 BTC (this unit is called as SATS; 1 BTC equals 10^8 SATS). In India, you can buy Bitcoin for even INR 10. BTC is therefore set up for micro transactions at scale in the future.

Price and adoption

BTC is trading at $47,700 today (Oct 2, 2021) – an equivalent of INR 37 lakhs. BTC’s price, though volatile, has grown consistently year on year. If you had invested

INR 1,000 in BTC on Jan 1, 2016, it would be worth INR 1,09,791 today. On a shorter time frame of weeks or months, it is difficult to predict BTC’s price actions though as an investor with a 4 to 5 year horizon, you are likely to grow your wealth considerably with BTC.

More than 120 million users in the world have an exposure to cryptocurrencies today of which around 75 million are estimated to own some amount of BTC. This means, on average, every user owns 0.25 BTC. Analysts expect cryptocurrency adoption to grow 10x in the next 4-5 years aided by strong youth economies such as India. Therefore, the average BTC holding will likely drop to 0.025 BTC in five years. It is clearly anadvantage for early adopters today to enter positions in BTC at a lower price point.

Cryptocurrency market capitalization

Bitcoin has been the leader in the world of cryptocurrencies in spite of thousands of new coins/tokens being launched over the years. In terms of market capitalization, the cryptocurrency market is just above $2 trillion today. BTC represents more than 43 per cent of the market – this metric is called Bitcoin Dominance. This metric moves in cycles in the range of 40 to 70 per cent. At the starting of this year, BTC’s dominance was around 70 per cent. In the last quarter of this year, BTC dominance is expected to increase to up to 60 per cent as investor monies flow into this asset over all other cryptocurrencies.

The cryptocurrency market capitalization is about 2 per cent of what is invested in stocks and equities globally and hence there is potential to grow at least 5x in the next few years. BTC will be the dominant and safest crypto that drives this growth story.

Safety and regulation

The Bitcoin network has been live 24x7 for the past 12 years with no outage or erroneous transaction identified ever. The system is supported by millions of interconnected computers similar to the internet and is robust with no individual person having any control over the system.

Governments have been vary of adopting Bitcoin in the past but are slowly embracing this technology as user adoption grows. Developed countries such as the US, UK, Japan and Australia have regulated investments in this asset. El Salvador, a Central American nation, has made Bitcoin as legal tender in the country with more such countries planning along these lines. India has proposed a regulation around this that may fruition by early next year.

Overall, Bitcoin is a safe asset with enormous potential to grow in the upcoming years. 2021 is still considered early for this new age technology as mainstream adoption is bound to explode along with positive regulations for the asset class around the world.

Disclaimer:

Crypto-asset or cryptocurrency investments are subject to market risks such as volatility and have no guaranteed returns. Please do your own research before investing and seek independent legal/financial advice if you are unsure about the investments.

Uses of COVID Vaccine Certificate

Why do I need a vaccination certificate?

A COVID Vaccine Certificate (CVC) issued by the government offers an assurance to the beneficiary on the vaccination, type of vaccine used, and the provisional certificate also provides the next vaccination due. It also is an evidence for the beneficiary to prove to any entities which may require proof of vaccination specially in case of travel. Vaccination not only protects individuals from disease, but also reduces their risk of spreading the virus. Therefore, there could be a requirement in future to produce certificate for certain kind of social interactions and international travel.

Sankarabharanam Song in Tamil, Telugu, and Meaning in English

Sankarabharanam Song : Shankara nada shariraa Lyrics

Movie Name : Sankarabharanam

Language: Telugu

Singer (S) : SP Balasubhramanyam

Lyricist : Veturi Sundara Rama Murthy

Producer: Edida Nageswara Rao

Music Composer: KV Mahadevan

Director : K Vishwanath

Dialogues: Jandhyala

Actors : Manju Bhargavi

Banner: Poornodaya Art Creations

Release Date: 1979

சங்கரா.... நாதசரீரா பரா..
வேத விஹாரஹரா..ஜீவேஸ்வரா..
சங்கரா..,நாதசரீரா பரா...

வேத விஹாரஹரா ஜீவேஸ்வரா..
சங்கரா...

உயிரும் நீ என,உடலும் நீ என,
உலகமே நீயே என...
மௌனத்திரை வீழ,ஞாப்பிறை எழ,
நாதமே/தேகமென...
உயிரும் நீ என உடலும் நீ என
உலகமே நீயே என...
மௌனத்திரை வீழ/
ஞாப்பிறை எழ நாதமே தேகமென...
நாதம் பாடிட, நான் உன்னை போற்றிட
உன் பதம் மலர் பணிந்தேனே...
நாதம் பாடிட, நான் உன்னை போற்றிட
உன் பதம் மலர் பணிந்தேனே...
யாதுமான சிவ ஜோதியாய் ஒளிரும்
கண்டனே நீல கண்டனே....
தீமை நீங்கிட நன்மை ஓங்கிட,
நீதி காத்திட அவதரித்துவ,அவதரித்துவா/
சங்கரா நாதசரீரா பரா....
வேத விஹாரஹரா..ஜீவேஸ்வரா...
சங்கரா...

தகதக தகவென மின்னும் மின்னலும்
நெற்றிக் கண்ணன் புன்னகையோ
சலசல சலவென மழையாய் விழுவது
சங்கர சலங்கைகள் மணிதானோ...
தகதக தகவென மின்னும் மின்னலும்
நெற்றிக் கண்ணன் புன்னகையோ.
சலசல சலவென மழையாய் விழுவது/
சங்கர சலங்கைகள் மணிதானோ...
பரமனின் தலையிலே எழும் கங்கா.,
பாவம் தீர்க்கவே விழும் கங்கா....
பரமன் தலையிலே எழும் கங்கா,
பாவம் தீர்க்கவே விழும் கங்கா,
நான் பாடி அழுகிறேன் வருவாயே.,
ஆனந்த காட்ச்சி நீ தருவாயே......
ஆஆஆஆ,ஆஆஆஆ,ஆஆஆஆஆ

சங்கரா நாதசரீரா பரா..

வேத விஹாரஹரா ஜீவேஸ்வரா...
சங்கரா..,சங்கரா..,சங்கரா...

Song : Shankara nada shariraa 

Sankaraa…. Naada sareera para…

Sankaraa…. Naada sareera para…

Veda vihaara haraa… jeeveswaraa…

Sankaraa…. Naada sareera para…

Veda vihaara haraa… jeeveswaraa…

Sankaraa….

Praanamu neevani gaanamey needani.. praanamey gaanamani…

Mouna vichakshana Dhyaana vilakshana.. raagamey yogamani

Praanamu neevani gaanamey needani.. praanamey gaanamani…

Mouna vichakshana Dhyaana vilakshana.. raagamey yogamani

Naadopaasana chesina vaadanu nee vaadanu nenaithe…

Naadopaasana chesina vaadanu nee vaadanu nenaithe…

Dhikkareendhrajitha himagireendrasita kandhara.. neelakandhara…

Kshrudhrulerugani rudraveena ninnidra gaanamidi avatharinchara vini tarinchara

Sankaraa…. Naada sareera paraa…

Veda vihaara haraa… jeeveswara…

Sankaraa….Aa..Aa.aaa..

Merise merupulu murise pedhavula chiru chiru navvulu kaabolu..

Urime Urumulu sari sari natanala… siri siri muvvalu kabolu

Merise merupulu murise pedhavula chiru chiru navvulu kaabolu..

Urime Urumulu sari sari natanala… siri siri muvvalu kabolu

Paravasana sirasooganga.. dharaku jaarena siva ganga…

Paravasana sirasooganga.. dharaku jaarena siva ganga…

Na gaana lahari nuvvu munuganga…

Aananda vurshtine tadavgaa….Aaa…

Sankaraa…. Nadha sareera para…

Veda vihaara haraa… jeeveswara…

Sankaraa….Sankaraa…..Sankaraa…..

Translation into English

Sankaraa naadha shareeraa paraa

Veda vihaaraharaa jeeveshwara (2 times)

[Sankara! O wonderful embodied form of the unmanifest cosmic vibration, Om! (you are the universe). Hara(Shiva), You are the very abode of the sacred Vedas, and the Lord of all life forms.]

Praanamu neevani gaaname needani

Praaname gaanamani

Mouna vichakshana gaana vilakshana

Raagame yogamani (2 times)

[You are the life on earth. Songs are Your creation. Life is like a song. Silent introspection enlightens us to the truth that singing divine songs is a way to reach the higher spiritual elevation.]

Naadhopaasana chesina vaadanu

Nee vaadanu nenaithe (2 times)

[I will sing Your glories forever, I would like to be called Your faithful servant.]

Dhikkarendrajita himagirindrajita sita

Kantha ra neelakanta raa

Kshudhrulerugani rudraveena

Nirnidhra gaanamidi avatarinchara vini tarinchara (Sankaraa)

[O Lord Sankara, the lord of all directions, the one who resides on the lofty peaks of the Himalayas! O Lord, who is handsome because of a beautiful Blue coloured throat (because he swallowed the most dangerous poison to save this universe)! My song is like the eternal music from Rudraveena about which demons would not know, please come here, listen and enjoy the song.]

Merise merupulu murise pedavula

Chiru chiru navvulu kavolu

Urimey urumulu sari sari natanala

Siri siri muvvalu kavolu

[The dazzling lightning is, perhaps the smile of response (of my praise) on Your lips. The roaring thunders are perhaps the chimes from Your golden anklets while You dance in tune (to my song).]

Paravashaana sira suvuganga

Dharaku jaarenaa shiva gangaa (2 times)

Naa gaanala harinu munugangaa

Aananda vrishtine tadavangaa

[Mesmerized by my song, You nodded Your head blissfully, and the holy river Ganga, bound in Your dreadlocks slipped to Your forehead (and therefore onto the Earth, in the form of torrent). While You were immersing yourself in my song, I soaked in the happy rain (your blessings) which showered onto the Earth.]

Where was Mahatma Gandhi when India became independent?

Where was Mahatma Gandhi on 15 August, 1947 when India became independent?

On 15 August 1947, when the day of independence finally arrived, it was celebrated with gusto all over the country. But in Calcutta, a perturbed Gandhi was trying hard to end the violence that had torn the nation apart.

Gandhi refused to participate in any festivities - along with his protege Abdul Ghaffar Khan, he was the last person to fight Partition till the very end. "I cannot rejoice on August 15. I do not want to deceive you. But at the same time I shall not ask you not to rejoice. Unfortunately the kind of freedom we have got today contains also the seeds of future conflict between India and Pakistan. How can we therefore light the lamps?" Gandhi had said in July.

On 9 August, Gandhi arrived in Calcutta (as Kolkata was known then) with plans to move to Naokhali (now in Bangladesh) - a district torn by communal massacre and violence. In Calcutta, leading figures urged Gandhi not to continue to East Bengal. They felt if Gandhi could bring peace to Calcutta, peace would be restored in all of Bengal.

Gandhi then decided to stay at Hyderi Manzil, close to a Muslim dominated slum called Miabagan. There, he received hundreds of visitors and held prayer meetings. There were constant protests of "Gandhi go back" outside, as some felt Gandhi unduly sympathised with Muslims.

From 13 August onwards, Gandhi began efforts to personally pacify people from either community and urge them to end the violence. On many occasions, angry mobs refused to bow down, but Gandhi continued his efforts. Within days, the result was visible for everyone to see. Lord Mountbatten, noting this, wrote "In the Punjab we have 55 thousand soldiers and large-scale rioting on our hands. In Bengal our forces consist of one man, and there is no rioting."

On 15 August Gandhi marked the day with a 24 hour fast, prayer, and spinning yarn. "My way of celebrating great events, such as today's, is to thank God for it and, therefore, to pray," he wrote to his Quaker friend Agatha Harrison. When C Rajagopalachari visited and congratulated Gandhi for restoring peace in the city, Gandhi said he will not be satisfied "until Hindus and Muslims felt safe in one another's company and returned to their own homes to life as before."

Gandhi had further planned to travel to Delhi, then move on to Punjab, and eventually to Lahore, and thus bit by bit bring peace to entire country. Sadly, what eventually ended the violence was the shock and horror of Bapu's murder.

From: http://www.catchnews.com/national-news/where-was-mahatma-gandhi-on-15-august-1947-when-india-became-independent-1439554780.html

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From: 

https://www.youtube.com/watch?v=B9wPtFpbzvs&feature=youtu.be&ab_channel=GoogleAdSense