Are you smarter than me? 28 Angry Birds

Algebra Level 4

Two sportsman $A$ and $B$ went out for hunting and brought home 10 birds. The sum of squares of the number of shots fired by each was 2880, and the product of the number of shots fired by each was 48 times the product of number of birds killed by each. If $A$ had fired as often as $B$ and $B$ as often as $A,$ then $B$ would have killed 5 more birds than $A.$ If the number of birds killed by $A$ and $B$ are $a$ and $b,$ respectively, then what is the value of $ab(a-b)-b?$

The answer is 44.

2 solutions

Jatheen Varma Buddharaju
Jan 8, 2015

Let the number of shots fired by A and B be x and y.

Let the number of birds killed by A and B be respectively a and b.

Given $x\times x + y \times y = 2880$ . ----- (1)

Also given $x\times y = 48 \times ab$

The values of x and y which satisfy the condition (1) is 48 and 24.

Equating $48 \times 24$ to $48 \times ab$ , product of $a$ and $b = 24$ . We also know $a+ b = 10$

So, the values of $a,b$ can be $6,4$ or $4,6$ .

The last condition given eliminates 4,6 as below.

If the no of shots fired by A and B are switched then B kills 5 more than that of A, that is $3,8$ .

So A fired more shots and killed more birds, so the values of $a,b$ are $6,4$ .

So $(a-b) \times (ab) - b = (6-4) \times (6\times 4) - 4 = 44$ .

Mehul Chaturvedi
Dec 17, 2014

Solve and get

A killed $6$ and B killed $4$

Is there any one who could prove this

Since 10 bird are killed, only solution is 48 shoots killed 6 birds and 24 shoots killed 4 birds. Thus the rate of killing for 6 bird killer is 8 shoot per bird, 4 birds killer has a rate of 6 shoot per bird . When the shoots are interchanged, The 6 bird killer will kill 24/8=3 and $\color{#D61F06}{\text{4 bird killer will kill 48/6=8 birds so he is B } }$ means A killed 6 birds.

Niranjan Khanderia - 6 years, 3 months ago

Are you smarter than me? 28 Angry Birds

The answer is 44.

2 solutions

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