Question

Sachin scored 12000 in certain innings of its. In next five matches he manage to score just 95 runs such that his avg decreased by 1. Then what is the total no. of matches played by him?​

Answer 1

The total no. of matches played by him = 205

Step-by-step explanation:

Given:

Sachin scored 12000 runs in certain innings

He scored 95 runs in next 5 matches such that his average decreased by 1

To find out:

The no. of matches played by Sachin

Solution:

Let Sachin scored 12000 runs in x innings

Average after x innings = 12000/x

According to the question

$\frac{12000+95}{x+5}=\frac{12000}{x}-1$

$\implies 12095x=12000(x+5)-x(x+5)$

$\implies 12095x=12000x+60000-x^2-5x$

$\implies x^2+100x-60000=0$

$\implies x^2+300x-200x-60000=0$

$\implies x(x+300)-200(x+300)=0$

$\implies (x+300)(x-200)=0$

$\implies x=200, -300$

But the number of innings cannot be negative

Hence x = 200

Total no. of matches played by him = 200 + 5 = 205

Hope this answer is helpful.

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Answer 2

Given :  Sachin scored 12000 in certain innings of its. In next five matches he manage to score just 95 runs such that his avg decreased by 1.

To Find : What is the total no. of matches played by him?​

Solution:

Total Matches played  = T

Score = 12000 + 95 = 12095

Average = 12095/T

Scored 12000  in T - 5  

Average = 12000/(T - 5)

12000/(T - 5)  =  12095/T  + 1  

=> 12000T  = 12095(T - 5)  + T(T - 5)

=> 12000T  = 12095T - 60475 + T² - 5T

=>  T²  +90T -   60475 = 0

=>  (T + 295)(T - 205) = 0

=> T  = 205

205 Matched played together

200 matches played till he made 12000

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