A precious stone worth Rs. 19200 is accidentally broken into three pieces; the weights of the three pieces are in the ratio 4: 5: 7. The value of the stone is proportional to the squares of its weight. Find the total loss after it is broken.

When the stone breaks, its total weight remains the same but the value decreases because value is proportional to the square of weight. Original value: k*(16x)² = 256kx². After breaking: k*(16x²+25x²+49x²) = 90kx². Loss = 256kx² - 90kx² = 166kx² = (166/256)*19200 = Rs. 12450. The key insight is that (a+b+c)² > a²+b²+c², so breaking always reduces value when value depends on square of weight.