The total amount of sand contained in Boxes A, B and C is 360 grams. F

Question

The total amount of sand contained in Boxes A, B and C is 360 grams. First, 1/6 of the sand from Box A is poured into Box B. After that, 1/3 of the sand from Box B is poured into Box C. Finally, 1/5 of the sand from Box C is poured into Box A. At the end, each box has an equal amount of sand. How much sand did each box A, B and C, respectively have at the beginning?

A. 96, 168, 96

B. 102, 168, 90

C. 108, 156, 96

D. 108, 162, 90

E. 114, 162, 84

A. 96, 168, 96

B. 102, 168, 90

C. 108, 156, 96

D. 108, 162, 90

E. 114, 162, 84

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dimri10 · Answer

i get D, but i can only use backsolving.
assumption is that at the end

A IS 120 
B is 120
C is 120

4/5 of c (after distribution feom a and b) in order to be 120 are 150.
so 30 were contributed to A 
so A got 30 before becoming 120, so it was 90. 90 is afterdistributing 1/6 to B so a had actually 108. so only C-D.

now 5/6 *(18 (the part from a)+b)=150 to make b 162.

saurabh851 · Answer

Ans: D

Hint look for divisibility---
108 divided by 6 gives 18,
18 adds up to 162 and sum is divided by 3 gives 60,
60 adds up to 90 and sum is divided by 5 gives 30...

Hope it clears...

Lipun · Answer

After all transfers the sand contained in each box is equal to 120 gms.

=> 4/5*C = 120 => C = 150 and C/5 = 30

and, 2/3*B = 120 => B = 180 and B/3 = 60 => C = 150 - 60 = 90

and, 5/6*A + C/5 = 120 => 5/6*A + 30 = 120 => A = 108 => B = 162

So, A = 108, B = 162, and C = 90 at the beginning.

ScottTargetTestPrep · Answer

Solution:
 
We can let a, b and c be the amount of sand in boxes A, B and C originally. We can create the equations (notice after sand is transferred between the boxes, each box at the end has an equal amount of same, i.e., 360/3 = 120 grams of sand) :

5a/6 +   * 1/5 = 120

(b + a/6) * 2/3 = 120

and

* 4/5 = 120

Multiplying the second equation by 3/2, we have:

b + a/6 = 180

Substituting this in the third equation, we have:

* 4/5 = 120

c + 60 = 150

c = 90

Substituting 90 for c and 180 for b + a/6 in the first equation, we have:

5a/6 +   * 1/5 = 120

5a/6 + 150 * 1/5 = 120

5a/6 = 90

a = 90 * 6/5 = 108

Since only choice C has a = 108 and c = 90, the correct answer must be D (we will leave it to the reader to show that b = 162).

Answer: D

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The total amount of sand contained in Boxes A, B and C is 360 grams. F

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The total amount of sand contained in Boxes A, B and C is 360 grams. F

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