India vs Pak

Algebra Level 4

India after finishing their batting , challenged a target of 300 300 runs in 50 50 overs against Pakistan in cricket World Cup 2015 2015 .Now , to win the match , Pakistan had to do 301 301 runs in 50 50 overs. However , Pakistan did not manage to catch upto 301 301 runs but all their players were out when they made 224 224 runs. At that time , 3 3 overs were still remaining. Let R 1 R_1 be the required run-rate for Pakistan to win the match by scoring the runs to win the match runs in 3 overs, R 2 R_2 was their current run-rate .

If R 1 R 2 R_1 - R_2 can be expressed as a b \frac{a}{b} where , a , b a , b are co-prime positive integers , Find a + b a + b

D e t a i l s Details A n d And A s s u m p t i o n s : Assumptions: R u n R a t e = N u m b e r , o f , r u n s , m a d e O v e r s , c o n s u m e d RunRate = \frac{Number,of,runs,made}{Overs,consumed}

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The answer is 3088.

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1 solution

Nihar Mahajan
Feb 16, 2015

Pak had to make 301 224 = 77 301 - 224 = 77 runs in 3 3 overs to win the match.

Hence , R 1 = 77 3 \large R_1 =\large \frac{77}{3}

Pak had made 224 224 runs in 47 47 overs.

Hence , R 2 = 224 47 \large R_2 =\large \frac{224}{47}

Thus , R 1 R 2 = 77 3 224 47 = 77 × 47 224 × 3 47 × 3 = 3619 672 141 = 2947 141 \large R_1 - R_2 =\large \frac{77}{3} - \large \frac{224}{47} = \large \frac{77 \times 47 - \large 224 \times 3}{47 \times 3} = \large \frac{3619 - 672}{141} = \large \frac{2947}{141}

Therefore, a + b = 2947 + 141 = 3088 \large a + b = 2947 + 141 = \boxed {3088}

Brilliant way to troll. Hope India win against SA.

Bhaskar Sukulbrahman - 6 years, 3 months ago

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INDIA have never won against South Africa in World Cup.Hope this time we break the STREAK.

Atharva Sarage - 6 years, 3 months ago

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Last world cup India was winning , but was lost as Dhoni gave the last over to Ashish Nehra! :(

Nihar Mahajan - 6 years, 3 months ago

Yeah we finally did and SA streak ended.....

Rishabh Mishra - 6 years, 3 months ago

6-0,now that's a football score :p

Rifath Rahman - 6 years, 3 months ago

Why was this 100 points? >.<

Mehul Arora - 6 years, 3 months ago

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May be many people in other countries are not familiar with cricket terms much.:(

Nihar Mahajan - 6 years, 3 months ago

I don't know. I submitted it as Level 1. O.o

Nihar Mahajan - 6 years, 3 months ago

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What......>?!?

Mehul Arora - 6 years, 3 months ago

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@Mehul Arora Cricket game is played in very less countries.Many people are not familiar with cricket , its rules , how it is played , etc. hence points for these are increasing due to lack of experience , Like we Indians have.

Nihar Mahajan - 6 years, 3 months ago

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@Nihar Mahajan why we indians have experience as it shows in this world cup 2015

Mayank Raj - 6 years, 3 months ago

hope india reach finals

Mayank Raj - 6 years, 3 months ago

Let R 1 R_1 be the required run-rate for Pakistan to win the match by scoring 301 runs after 47 overs. So R 1 R_1 =301/47. Please not the words ""after 74 over". I think mine is the correct interpretations!!

Niranjan Khanderia - 6 years, 3 months ago

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Actually in a one day cricket game you get 50 overs to chase the runs set up by the oppositions,but Pakistan didn't have 2 batsmen left to bat,that's why their innings ended before finishing their all whole 50 overs

Rifath Rahman - 6 years, 3 months ago

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The point is the rate has to be over 47 overs. R 1 R_1 is based on 47 over not 3 overs left. The wordings are "Let R 1 R_1 be the required run-rate for Pakistan to win the match by scoring 301 runs after 47 \color{#D61F06}{47} overs. ""

Niranjan Khanderia - 6 years, 3 months ago

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@Niranjan Khanderia So , you think that the phrase 'after 47 overs'must be removed? If so , I apologize for the misconceptions and would edit the solution.Thanks

Nihar Mahajan - 6 years, 3 months ago

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@Nihar Mahajan No. I think t he phrase is OK. The answer should be based on it. That is my view. Better moderator may advice.

Niranjan Khanderia - 6 years, 3 months ago

@Nihar Mahajan Yes the language and phrasing of the problem was not clear until I saw the solution.. it should have been like " let R1 be the run rate required to win the match in the remaining 3 overs assuming Pakistan had wickets in hand"

Afzal Noor - 6 years, 3 months ago

@Niranjan Khanderia Oh,if it was"Let R1 be the 77 runs Pakistan needs to score from the remaining 3 overs" would've been better

Rifath Rahman - 6 years, 3 months ago

i will be waiting for a s. Africa vs India problem next weekend

Arnav Das - 6 years, 3 months ago

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