Troop Loss
As Napolean retreated from moscow, he was pursued by General Janvir through deep snow and blinding blizzards. At the first skirmish the General Janvir lost 20% of his troops. At the second skirmish he lost 20% of those left. If the lost count was 7,200 men, How many did he start with ?
Labels: mathemagic
posted by Rajesh Lal at
8:58 AM
22 Comments:
20% of 100
+
20% of 80
=
20+16 = 36%
7200 = 36%
100% = 20000
correct me if i'm wrong...
Unless i read it wrong, it should be 18000 troops.
20%+20%= 40%...
7200=40% of 'x'.
7200=.40x
divide by .40
18000=x
Oh.
I did read it wrong.
20% of the ones leffttt lol im stupid XD
I came up with 11,250.
11250-20%=9000
9000-20%=7200
x = total troops:
20%*x = # of troops lost in 1st skirmish
20%*(x-20%*x) = # of troops lost in 2nd skirmish
Total lost troops:
20%*x + 20%*(x-20%*x) = 7200
Solve for x: x = 20,000. Emily's way was prettier.
total-7200=(100%-20%)/20%
20%=1/5
4/5 left
1/5th of 80%=16%
20%+16%=36%=7200
36/100=9/25
9/25=7200/total
(7200*25)/9=20000
20000 troops is what he started with
10 368
(7200/80)*20 = 1800
(1800+7200) = 9000
(9000/80)*20 = 2250
(2250+900) = 11250 <----final answer
-Rx
sorry i mis-read the thing...
(7200/20)*100 = 36000 ---> 2nd skirmish
(3600/80)8100 = 45000 ---> 1st skirmish
therefore... he had 45000 to begin with
-Rx
Well, I wish adding percentages worked as nicely as Emily made it seem... but using the old "check your work" method, it's wrong, and 11250 is right...
20,000 * .2 = 4000
16,000 * .2 = 3200
16,000 - 3200 = 12800 != 7200
I just let 80% be 4/5, and solved:
4/5*(4X/5) = 7200 -- and X = 11250
i thought that too but the question states that the LOST count is 7200 which means that that was the number of ppl that died in the second skirmish.. not the number of ppl that was left.
-Rx
whoops... darned that careful reading...
18,000
7,200 = 40%
3,600 = 20% ... x5 = 100%
(.8*7200) = 9000
(.8*9000) = 11,250
11,250+7250 = 20,000
20,000 is what I get too.
This can be simplified.
20% = 1/5
so to work back just add 1/4 or 25%
7200 + 1800 = 9000
9000 + 2250 = 11250
So anyone saying 11250 is correct.
I came up with 20,000.
Jayne is correct (and others with 20,000), I didn't pay attention!
Lost count is 7,200 which was from 36% of the original so must have been 20,000.
Darn silly person me.
@ bob uppendown
but is your reverse it:
20000*0.8 = 16000
16000*0.2 = 3200
of course if you use emily's way you get 20,000 but if you check it step by step its a different answer... now i dont know the real answer... maybe napoleon never fought Gen Janvir.. or mebbe he aint no general
20,000 is correct.
20(20,000/100) = 4000
20,000 - 4,000 = 16,000
20(16,000/100) = 3,200
16,000 - 3200 = 12,800
4000 + 3200 = 7200
7200 + 12,800 = 20,000
7200 represents 80% of troops after the 2nd attack.
(7200/80)X100 = 9000 = total troops before the 2nd attack.
9000, therefore, represents 80% of the troops after the second attack.
(9000/80)X100 = 11,250 = total troops to begin with.
To prove this is correct follow the calculation in reverse.
(11,250 X 0.8) = 9,000 = a 20% loss
(9,000 X 0.8) = 7,200 = a further 20% loss.
Therefore 11,250 is the correct answer.
StabiloBoss
Correction - fourth line should read *9,000, therefore, represents 80% of the troops after the first attack.* Tks
StabiloBoss
the way i read it, he lost 20% from his initial 100%, then another twenty% from 80% of his troops. 20% of 100% is 80%. 20% of 80% is 16%. So he must have lost 16% of his troops. 7200 is 16% of 45,000. I think he had 45,000 troops but i could be wrong....
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