precious stone breaks into four pieces having weights in the proportion 1:2:3:4 The value of such stone is proportional to the square of its weight.what is the percentage loss incurred due to breaking?
Answers
Answer:
70%
Step-by-step explanation:
Precious stone breaks into four pieces having weights in the proportion 1:2:3:4 The value of such stone is proportional to the square of its weight.what is the percentage loss incurred due to breaking?
Let say Stone weight was = 10 W
Value of Stone ∝ Weight²
=> Value of stone = k (10W)² ( k is a constant)
=> Value of original stone = 100kW²
stone breaks into four pieces having weights in the proportion 1:2:3:4
So weight are W , 2W , 3W & 4W
Value of W stone = k (W)² = kW²
Value of 2W stone = k (2W)² = 4kW²
Value of 3W stone = k (3W)² = 9kW²
Value of 4W stone = k (4W)² = 16kW²
Total Value of 4 stones = kW² + 4kW² + 9kW² + 16kW² = 30kW²
Value lost = 100kW² - 30kW² = 70kW²
% Loss = (70kW² / 100kW²) * 100 = 70%
70% Value loss occurred due to breakage of precious stone
Answer:
simply done!
Step-by-step explanation:
let assume the whole initial value be 100 ( percent is given that's why).
Proportions after broken are given 1:2:3:4.
Given, value is proportional to square of weight.
So ,let weight of first piece 1g.
second 2g.
third 3g.
fourth 4g.
So ,value of first, second, third and fourth piece must be 1,4,9 and 16 respectively.
final value become= 1+4+9+16=30.
=>Loss = 100-30 = 70.
Hence answer is 70%.