Aptitude - Simplification - Discussion

B kills once in 2 shots.

No. of failure shots = 1.

No. of succeeded shots = 1.

When no. of failure shots = 27 then no. of succeeded shots = 27,

So, total no. of shots by B = 27+27 = 54.

When B shoots 3 shot then A shoots 5 shots.

So, When B shoots 1 shot then A shoots 5/3 shot.

So, When B shoots 54 shot then A shoots 54*5/3 = 90 shots.

When A shoots 3 it killed 1.

So, when A shoots 90 it killed = 90/3 = 30.

Thanks for explaining the answer @Hary.

• B kills once in 2 shots ⇒ B’s hit probability = 1/2. So miss probability = 1 - 1/2 = 1/2.
• B has missed 27 times. Since each shot has a 1/2 chance to miss, the number of shots B fired is
shots by B = 27/(1/2)= 27*2 = 54.
• A fires 5 shots for every 3 shots of B. So when B fired 54 shots, A fired
shots by A = (5/3)*54 = 5*18 = 90.
• A kills once in 3 shots, so the number of kills by A = 90/3=30.

Answer: 30 birds (option A).

A-27*5=135,
b-27*3=81,
a-b=135-81,
=54/3=18,
A-18*5=90,
A=90/3=30.

Well explained, Thanks @Smrithi.

Thanks @Sudip.

It is given that if A fires 5 shots B fires only 3 times.
It is given that p(A)=1/3 and p(B)=1/2.

It is also given that A missed 27 times so he fired totally 54 times.
From the above we can calculate that totally A fired 90 times.

So total successful firings by A=90*1/3=30.

Thanks @Sudip.

Every time B fires 3 shots, A fires 5 shots
That’s a firing ratio: A: B = 5 : 3, every time B fires 3, A fires 5.
But B, from 3 shots, he misses 1 shot every time he fires and kills 2, so the total he misses is 27.
In simple language, B misses 1 shots and kills 2, We have given no of shots he missed, but it doesn't include the shots he used to kill, which is 2.
To get the total no of shots of B, 27x2=54 shots.
To calculate A shots, which is 5:3, 54/3=18 times A fired, and 1 time firing consists of 5 shots.
So, 18 x 5 = 90.
The total no of shots A fired is 90, kills once in 3 shots, so 90/3= 60.

How is the no. of failure shots equal to the no. of succeded shots.. i.e. 3x/18=27??