A Geometric Puzzle

Find the area enclosed by the 4 arcs in the figure (shaded in grey)

The figure is drawn as below

1. A square is drawn with side "a'

2. With the side of square as radius, 4 quadrants are drawn with centre at each of the vertices.

Gold Import Duty Raised!

This was the news of the day.  Import duty on gold raised from 4% to 6%.  And, just a day after that announcement, Govt. followed with another one, raising the import duty of raw gold (called Dore, an alloy of gold and silver) from 2% to 5%.   News Item in Live Mint: http://goo.gl/JWQmh

Reason: Controlling the Current Account Deficit.

What is Current Account Deficit? 

It is the amount by which the total imports exceed the total exports.  A country having current account deficit imports more (goods and services) than what it exports and owe the rest of the world from revenues generated within the country.

Why increase import duty on gold?

India imports approximately 900 tonnes of gold per year.  That is approximately 20% of Annual Gold Demand of around 4500 tonnes. (Data: World Gold Council, Demand Trends http://www.gold.org/investment/research/regular_reports/gold_demand_trends/ ).  As quoted from this article (http://goo.gl/7KXaA) of Live Mint Gold imports constituted 11.5% in India's total imports basket in 2011-12 in value terms, growing from 6.9% in 2008-9.\

This means there is a drastic increasing trend in gold consumption.  Gold does not contribute greatly to the real economy of the country - as most of gold imports are for jewelry and coins which get promptly stored in households and safety lockers.  See this article by Nilesh Shah on Indian consumers crazy appetite for gold http://goo.gl/lZA2z  He warns that if Indians stop buying gold, the gold bullion market may crash (and such a price correction may in fact be welcome)

Can I do something as a retail investor?

Yes, one can reduce the consumption of gold.  Or to put in better words - look for investment opportunities other than gold.  Because, the gold investment habit of Indian housholds is costing the country dearly in terms of widening the current account deficit.  And, Govt. of India, at this point is signalling the same to the investors.  It is up to the individual investors to take cue and act accordingly.

KXIP v CSK Preview

With a win against MI, now KKR is also into the final four!

Tomorrow's KXIP v CSK match may produce a third semifinalist in CSK. But, if KXIP wins, then CSK will join RCB, RR and KXIP in 20+ % chance of making it to semi-finals.  A loss for KXIP and their semi-final spot is gone for sure!

MI, RR, RCB, KXIP - all want CSK to lose!

Team	Current Chance		KXIP v CSK
		KXIP wins	CSK wins	No Result
DD	100.00	100.00	100.00	100.00
CSK	64.06	28.13	100.00	81.25
DC	0.00	0.00	0.00	0.00
RCB	18.75	25.00	12.50	25.00
MI	81.25	93.75	68.75	68.75
RR	21.88	25.00	18.75	25.00
KXIP	14.06	28.13	0.00	0.00
KKR	100.00	100.00	100.00	100.00
PWI	0.00	0.00	0.00	0.00

MI v KKR Preview

It is clear that CSK and RCB are least bothered about this match!  Though RCB may hope for a rare "no result" for this match, as that boost its chances of getting a semi-final spot.

RR wants KKR to win.

KXIP wants MI to win.

Team	Current Chance		MI v KKR
		MI wins	KKR wins	No Result
DD	100.00	100.00	100.00	100.00
CSK	64.06	64.06	64.06	64.06
DC	0.00	0.00	0.00	0.00
RCB	18.75	18.75	18.75	21.88
MI	90.63	100.00	81.25	96.88
RR	18.75	15.63	21.88	9.38
KXIP	16.41	18.75	14.06	14.06
KKR	91.41	82.81	100.00	93.75
PWI	0.00	0.00	0.00	0.00

DD v KXIP Preview

DD wins and they are through to the play-offs.  But, what happens to other teams with a Delhi win?

The table below looks at different results of this match and how that affects the chances of other teams to make to the semi finals.

Semifinal Chance %

Team	Current Chance		DD v KXIP
		DD wins	KXIP wins	No Result
DD	96.88	100.00	93.75	100.00
CSK	57.03	64.06	50.00	64.06
DC	00.00	0.00	0.00	0.00
RCB	20.31	18.75	21.88	18.75
MI	89.06	90.63	87.50	87.50
RR	17.58	18.75	16.41	16.41
KXIP	30.66	16.41	44.92	21.88
KKR	88.48	91.41	85.55	91.41
PWI	00.00	0.00	0.00	0.00

DD win improves the chances of CSK, MI, RR and KKR to get a semi-final berth.  Also, it is clear that only RCB will hope for a Kings XI's win in this match.

MI v RCB Preview

This blog post is updated, as there was an error in my calculation earlier.  Today's win will not take MI to semi-finals. Thanks to @rajeshstats for pointing out.

Mumbai Indians have their match against Bangalore today.  If MI wins this match, they are through to the play-offs!

Surprisingly, the other contenders for the play-off slots look forward to an MI win!

Here is the chance table.  This is based on the current points that the teams have gathered and on an assumption that the relative position of NRR does not change.

Team	Current Chance		RCB v MI
		RCB wins	MI wins	No Result
DD	97.85	98.44	97.27	97.27
CSK	36.04	33.01	39.06	33.01
DC	0.00	0.00	0.00	0.00
RCB	50.68	76.37	25.00	58.59
MI	74.46	56.74	92.19	76.17
RR	19.97	20.21	19.73	19.73
KXIP	28.61	24.71	32.52	24.71
KKR	92.38	90.53	94.24	90.53
PWI	0	0	0	0

Team	Current Chance		RCB v MI
		RCB wins	MI wins	No Result
DD	97.85	94.53	96.09	96.09
CSK	36.04	27.34	39.06	27.34
DC	0.00	0.00	0.00	0.00
RCB	50.68	68.75	23.83	52.34
MI	74.46	85.94	100.00	98.83
RR	19.97	12.30	14.26	14.26
KXIP	28.61	20.61	32.52	20.61
KKR	92.38	90.53	94.24	90.53
PWI	0.00	0.00	0.00	0.00