Question

cost of a diamond varies directly as the square of its weight.A diamond broke into four pieces with their weight in the ratio 1:2:3:4.If the loss in the total value of the diamond was Rs.70,000,the price of the original diamond was?​

Answer 1

Ratio of weights is 1:2:3:4

Ratio of costs 1:4:9:16

Let the smallest piece cost be x. Then the cost of other pieces is 4x, 9x, and 16x

Adding up we get total cost as 30x.

The weight of the original unbroken diamond would have been 1+2+3+4 that is 10 and its cost would be 100x

So the loss is 100x - 30x = 70x

Given that 70x = $70,000 we get x = $1000

Original price is 100x = $100,000

Answer 2

Step-by-step explanation:

the same answer but a little bit more detailed

we are given that cost=(weight)^2-directly as the square of the weight

and total piece was broken into four pieces

first let us find the total weight of initial piece

1k+2k+3k+4k=10k where k is +ve integer

so cost of intial piece=(10k)^2

then, let us find the cost of other pieces

p1. with weight k

cost=(k)^2

p2, with weight 2k

cost=(2k)^2=4k^2

p3. with weight 3k

cost=(3k)^2=9k^2

p4, with weight 4k

cost=(4k)^2=16k^2

total cost of pieces=k^2+4k^2+9k^2+16k^2=30k^2

and we are given that the value of broken pieces is 70000 less than initial total one

30k^2=100k^2-70000

70k^2=70000

k^2=1000

to find value of initial diamond simply insert k^2=1000 in expression fo its value

cost=100k^2=100*1000=100000

so A