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| An Apples And Boxes Puzzle (Posted on 2007-02-20) |
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A certain number of apples are kept in five boxes; Box 1, Box 2, Box 3, Box 4, Box 5 such that:
(i) The number of apples in Box 3 is one-sixth of the total apples in Box 5.
(ii) Box 2 has twice as many apples as Boxes 3 and 5 combined.
(iii) Box 1 has half as many apples as Box 5
(iv)Box 4 has 10 more apples than Box 1.
(v) Box 4 has 1/4 as many apples as Box 2.
Determine which boxes contain how many apples and the total number of apples in all the five boxes.
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Submitted by K Sengupta
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Rating: 3.0000 (2 votes)
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Solution:
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(Hide)
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(Box 1,Box 2, Box 3, Box 4, Box 5)
= (60, 280, 20, 70, 120)
The total number of apples in all the boxes is 550.
EXPLANATION:
Let the number of apples in Box i be B_i; i= 1,2,3,4,5
Then, we have:
(i)B_3 = B_5/6; (ii)B_2 = 2(B_3 + B_5);
(iii)& (iv)B_1 = B_5/2 = B_4 -10; (v) B_4 = B_2/4
B_5 = 6*B_3, so B_2 = 2*7*B_3 = 14*B_3= 4*B_4, and so:
B_4 = (7/2)*B_3.
Also, B_5 = 2*B_1, so that B_1 = 3*B_3
So, B_1 = B_4 -10 gives:
B_3/2 = 10, giving B_3 =20, so that:
B_1 = 3*20 = 60; B_2 = 14*20= 280
B_4 = (7/2)*B_3 = 70; B_5 =6*B_3 = 120
Total number of apples in all the boxes
= 60 + 280 + 20 + 70 + 120
= 550
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