IPL Fever #2

Algebra Level 3

In a match between Mumbai Indians and Rajasthan Royals, Rajasthan Require 165 runs to win off 20 overs.

However that is not the question.

At a certain period of time, When x x overs are left, The Rajasthan Royals require y y runs to win. If the RR (Rajasthan Royals. ) Score 3 runs in the next over, The run rate Increases by 1. If the required run rate when x x overs are left is 10 r.p.o, Find x + y x+y

Details and Assumptions

Run rate= R u n s R e q u i r e d N u m b e r o f o v e r s \dfrac {Runs Required}{Number of overs}

Rajasthan Royals and Mumbai Indians are IPL (Indian Premier league) Teams.

r.p.o= Runs per over. (Unit of run rate)


The answer is 88.

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2 solutions

Nihar Mahajan
Apr 14, 2015

By 1 s t 1^{st} condition ,

y x = 10 y = 10 x ( 1 ) \dfrac{y}{x}=10\\ \Rightarrow y=10x \dots (1)

By 2 n d 2^{nd} condition ,

y 3 x 1 = 10 + 1 y 3 x 1 = 11 y 3 = 11 x 11 11 x y = 8 11 x 10 x = 8 [Using (1)] x = 8 , y = 80 , x + y = 88 \dfrac{y-3}{x-1}=10+1\\ \Rightarrow \dfrac{y-3}{x-1}=11 \\ \Rightarrow y-3=11x-11 \\ \Rightarrow 11x-y=8\\ \Rightarrow 11x-10x=8 \text{[Using (1)]} \\ \Rightarrow\large\boxed{x=8 \quad , \quad y=80 \quad ,\quad x+y=88}

Why U always copy my solution? On a brighter side Great minds think alike! Hi5! :D

Mehul Arora - 6 years, 2 months ago

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I didn't copy :/ You have wrongly used the definition of runrate (you have used its reciprocal). -_-

Nihar Mahajan - 6 years, 2 months ago

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But i asssumed them to be the different variables first -_- Like, I interchanged variables.

Mehul Arora - 6 years, 2 months ago

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@Mehul Arora You have o v e r s r u n s \dfrac{overs}{runs} -_-

Nihar Mahajan - 6 years, 2 months ago

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@Nihar Mahajan Check it first. -_- Sorry for the late reply, Had slept.

Mehul Arora - 6 years, 2 months ago

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@Mehul Arora Now its correct... -_-

Nihar Mahajan - 6 years, 2 months ago

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@Nihar Mahajan okay -_- :P

Mehul Arora - 6 years, 2 months ago

@Mehul Arora So u mean 8 8 runs required in 80 80 overs ... -_-

Nihar Mahajan - 6 years, 2 months ago
Mehul Arora
Apr 14, 2015

Let The overs remaining =y

Let the Runs required=x

Therefore,

x y = 10.... ( 1 ) \dfrac{x}{y} = 10.... (1)

And After 1 over, Since the run rate becomes 11 (10+1),

x 3 y 1 = 11..... ( 2 ) \dfrac{x-3}{y-1}=11..... (2)

Now, From 1, We have x = 10 y x=10y

Substituting, We get,

10 y 3 = 11 ( y 1 ) 10y-3=11(y-1)

10 y 3 = 11 y 11 10y-3=11y-11

y = 8 y=8

Now Since x=10y, x = 80 x=80

Therefore, x + y = 88 x+y=88

Cheers! :D

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