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Two Ten Ton Tough Elephants

Question

Tenny and Tonny are two elephants. Every winter, Tenny gains ten percent of his body weight, and Tonny loses ten percent. Every summer, the opposite happens: Tenny loses ten percent and Tonny gains ten percent. This has gone on for ten years, and now they each weigh ten tons. How many tons did Tenny and Tonny weigh ten years ago?

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Let the initial weights of Tenny and Tonny were x ton & y ton respectively.

After 10 years Tenny will be 11^10x/10^10 ton.
& after 10 years Tonny will be 9^10y/10^10 ton.
Now they each weigh 10 ton (given).
So 11^10x/10^10 = 10 OR x = 10^11/11^10 ton
Similarly y = 10^11/9^10 ton

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11.0527 tons?

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Let the initial weights of Tenny and Tonny were x ton & y ton respectively.

After 10 years Tenny will be 11^10x/10^10 ton.

& after 10 years Tonny will be 9^10y/10^10 ton.

Now they each weigh 10 ton (given).

So 11^10x/10^10 = 10 OR x = 10^11/11^10 ton

Similarly y = 10^11/9^10 ton

Let the initial weights of Tenny and Tonny were x ton & y ton respectively.

After 10 years Tenny will be 11^10x/10^10 ton.

& after 10 years Tonny will be 9^10y/10^10 ton.

Now they each weigh 10 ton (given).

So 11^10x/10^10 = 10 OR x = 10^11/11^10 ton

Similarly y = 10^11/9^10 ton

OOOPS....I missed the changes in summer....

I shall again post the solution.

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Let the initial weights of Tenny and Tonny were x ton & y ton respectively.

After 10 years Tenny will be (9^10*11^10x)/10^20 ton.
& after 10 years Tonny will be (11^10*9^10y)/10^20 ton.
Now they each weigh 10 ton (given).
So, x = y = 10^21/(11^10*9^10) ton
Edited by bhramarraj
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Let the initial weights of Tenny and Tonny were x ton & y ton respectively.

After 10 years Tenny will be (9^10*11^10x)/10^20 ton.

& after 10 years Tonny will be (11^10*9^10y)/10^20 ton.

Now they each weigh 10 ton (given).

So, x = y = 10^21/(11^10*9^10) ton

But this differs with dark_magician,s answer, as my value comes to approximately 11.17 Ton.

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@brahmaraj - I may be wrong but i think there is mistake in your calculation, our answers are coming same.

Edited by dark_magician_92
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Commutativity of multiplication makes it irrelevant, I believe.

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Let's assume Winter since a year starts in January.

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11.0527 tons?

Did we write our decimals out of order? Because I got 11.05727... The difference is small though so I will still give you best answer.

90% of 110% of any number n is (.90)(1.10)(n) = 0.99 n . Same goes for 110% of 90%. So each year the elephants lose 1%; we multiply by 0.99 ten times, and we get (if n = orig. wt):
((0.99)^10) * n = 10 tons ;
n = 10 / (0.99)^10
= 10 / 0.904382075
= 11.05727355 tons.
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11.0527 tons?

Did we write our decimals out of order? Because I got 11.05727... The difference is small though so I will still give you best answer.

90% of 110% of any number n is (.90)(1.10)(n) = 0.99 n . Same goes for 110% of 90%. So each year the elephants lose 1%; we multiply by 0.99 ten times, and we get (if n = orig. wt):
((0.99)^10) * n = 10 tons ;
n = 10 / (0.99)^10
= 10 / 0.904382075
= 11.05727355 tons.

I did the same way as you have done, its just that i thought if i am right, writing till only 3-4 decimal places would be sufficient..

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11.0527 tons?

Did we write our decimals out of order? Because I got 11.05727... The difference is small though so I will still give you best answer.

90% of 110% of any number n is (.90)(1.10)(n) = 0.99 n . Same goes for 110% of 90%. So each year the elephants lose 1%; we multiply by 0.99 ten times, and we get (if n = orig. wt):
((0.99)^10) * n = 10 tons ;
n = 10 / (0.99)^10
= 10 / 0.904382075
= 11.05727355 tons.

I did the same way as you have done, its just that i thought if i am right, writing till only 3-4 decimal places would be sufficient..

you got .0527 where i got .0572. So i wasn't sure if you used a different strategy or inverted your numbers

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11.0527 tons?

Did we write our decimals out of order? Because I got 11.05727... The difference is small though so I will still give you best answer.

90% of 110% of any number n is (.90)(1.10)(n) = 0.99 n . Same goes for 110% of 90%. So each year the elephants lose 1%; we multiply by 0.99 ten times, and we get (if n = orig. wt):
((0.99)^10) * n = 10 tons ;
n = 10 / (0.99)^10
= 10 / 0.904382075
= 11.05727355 tons.

I did the same way as you have done, its just that i thought if i am right, writing till only 3-4 decimal places would be sufficient..

you got .0527 where i got .0572. So i wasn't sure if you used a different strategy or inverted your numbers

Whoops, sorry. I mistyped.

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