The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone?
A. 10%
B. 40%
C. 71%
D. 81%
E. 93%
I have been sweating on this question for hours now, it seems there is no solution. Can any expert help me out on this? i really appreciate.
Thank you in advance
Hi Roland2rule,
Let's take a look at your question.
If a big stone broke into three parts in the ratio 1:4:5.
Let the weight of the broken stones be 1 unit, 4 unit and 5 unit. Then the weight of the original stone must be 1 + 4 + 5 = 10 units.
Since, the value of a precious stone is directly proportional to the cube of its weight, therefore,
Value of original stone must be:
$$=\ 10^3=1,000$$
Value of the stone with weight 1 unit:
$$=\ 1^3=1$$
Value of the stone with weight 4 units:
$$=\ 4^3=64$$
Value of the stone with weight 5 units:
$$=\ 5^3=125$$
Total value of the 3 broken pieces = 1 + 64 + 125 = 190
Let's now find the percent decrease in the value.
$$=\ \frac{1,000-190}{1,000}\times100\%$$
$$=\ \frac{810}{1,000}\times100\%$$
$$=\ \frac{810}{10}\%$$
$$=\ 81\%$$
Hence, there is an 81% drop in the value of the stone.
Therefore, Option
D is correct.
Hope it helps.
I am available if you'd like any follow up.
