Aptitude Discussion

Q. |
A Batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning. |

✖ A. |
40 |

✔ B. |
39 |

✖ C. |
52 |

✖ D. |
55 |

**Solution:**

Option(**B**) is correct

Let the average after 17th innings = $x$

Then average after 16th innings = $(x-3)$

Therefore $16(x-3) + 87 = 17x$

Therefore $x = 39 $

**Edit:** For a quick allternative solution, check comment by **Sravan Reddy.**

**Sravan Reddy**

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Great Brother...Great Work...thank you a lot...

**Sachin**

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The statement is not properly defined according to your answer result. Please check it

**Mohan Dand**

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let avg after 17th ings $=x$

therefore avg after 16th ings $=(x-3)$

let total runs after 16th ings $=T$

now,avg after 16th ings =:

\(\Rightarrow\) total runs/no.of ings

\(\Rightarrow \dfrac{T}{16}=(x-3)\)

\(\Rightarrow\) now \(T=16(x-3)\)

now avg after 17th ings=:

\(\Rightarrow \dfrac{\text{total runs}}{\text{no. of innings}}\)

\(\Rightarrow T+\dfrac{87}{17}=x\)

\(\Rightarrow\) substitute $T$ value

\(\Rightarrow 16(x-3)+\dfrac{87}{17}=x\)

\(\Rightarrow\) after simplification we get \( x=39\)

One quick way to do it with mind for these type of problems (in less than 10 secs):

=> He was able to increase average by 3. That means he gave 3 runs to all his previous innings. So answer is $87 - (3 \times 16) = 87-48 = 39!!$

$\textbf{P.S.}$ If you did not understand the splitting 3 runs to all other innings here is an example.

Let the scores for 3 innings be 3,3,3 and fourth innings the average got raised to 4 by scoring 7.

That can be split as if he scored the average runs in the latest innings and distributed 1 run to all the previous innings.

So, the scores instead of 3, 3, 3, 7 will be 4, 4, 4, 4.

Sorry, if I confused you more but hope you will like it once you master this art of splitting :)