1. ## Helicopters

Under the scheme of rural development the OCP purchased t number of helicopters and these were allocated equally among 7 districts of Michigan and thus 4 helicopters remained unallocated. Similarly every district allocated these helicopters equally to 10 blocks in each district and still 3 helicopters remained unallocated in every district. Further every block assigned these helicopters equally to every 16 villages in each block and thus 2 helicopters per block remained unallocated. According to the scheme every village must receive atleast 1 helicopter.

1) Is it possible to determine the number of helicopters allocated to each block ? Please explain why and how.

2) If ,instead, OCP purchased k helicopters to provide exactly 1 helicopter to each village as mentioned in the scheme, but later on it sent one tractor to each village directly without the involvement any block or district, then the number of helicopters OCP has saved more in comparison to the previous scheme ? Please give explanation.

2. ## Re: Helicopters

This might have something to do with remainder theorem ! Though I am not sure !

3. ## Re: Helicopters

Originally Posted by Robocop
This might have something to do with remainder theorem ! Though I am not sure !
I don't think so! It is related to successive division and finding the divisor.

4. ## Re: Helicopters

Originally Posted by SPOCK
I don't think so! It is related to successive division and finding the divisor.

5. ## Re: Helicopters

The answer to the question (2) is 161 though I don't have the detail explanation of the answer. Request a detail explanation.

6. ## Re: Helicopters

Are you Swami Mathsananda ?

7. ## Re: Helicopters

Originally Posted by Robocop
The answer to the question (2) is 161 though I don't have the detail explanation of the answer. Request a detail explanation.
Would you like fries with that?

Are you Swami Mathsananda ?

8. ## Re: Helicopters

$\displaystyle t = 7q_1+4$
$\displaystyle q_1 = 10q_2+3$
$\displaystyle q_2 = 16q_3+2$

Plugging in backwards, we have:

$\displaystyle q_1 = 160q_3+23$

$\displaystyle t = 1120q_3 + 165$

Thus, the number of helicopters allocated to each block is $\displaystyle \dfrac{t-165}{1120}$.

Question 2 makes no sense. It does not seem to be asking anything. I think it meant, how many helicopters were unallocated by the districts, blocks, and villages. The answer to that is 161 (165-4 = 161).

9. ## Re: Helicopters

Originally Posted by Wilmer
Are you Swami Mathsananda ?
What Swami ? I am Alex Murphy a property of OCP from Detroit , Michigan !

10. ## Re: Helicopters

A "click-on" is worth a 1000 words:
Rural-development - My Math Forum

I'm "Denis" at that site.

11. ## Re: Helicopters

Originally Posted by Wilmer
A "click-on" is worth a 1000 words:
Rural-development - My Math Forum

I'm "Denis" at that site.
That swami or whatever his name is copied my question from this forum & he mailed me about an error in the second question where the text mentioned tractor it should be actually helicopter. Regret that error !
And I hope we can find the answer for the second question now.

12. ## Re: Helicopters

Originally Posted by SlipEternal
$\displaystyle t = 7q_1+4$
$\displaystyle q_1 = 10q_2+3$
$\displaystyle q_2 = 16q_3+2$

Plugging in backwards, we have:

$\displaystyle q_1 = 160q_3+23$

$\displaystyle t = 1120q_3 + 165$

Thus, the number of helicopters allocated to each block is $\displaystyle \dfrac{t-165}{1120}$.

Question 2 makes no sense. It does not seem to be asking anything. I think it meant, how many helicopters were unallocated by the districts, blocks, and villages. The answer to that is 161 (165-4 = 161).
Thanks SlipEternal ! The answer to question (1) is cannot be determined and I can see now why, because unless we know the value of t we cannot find the value of helicopters allocated to each block. Also for question no. (2) there is a minor error. It will be helicopters instead of tractors in the text.