The ratio of gold to copper in a bracelet is 4 : 7. If the price of copper is 1/10th the price of gold, find the cost of the bracelet if the cost of copper in the bracelet is 28000 rupees.
Rs. 188000
Let the amounts of gold and copper be \(4k\) and \(7k\) (ratio 4 : 7). Let the price of copper per unit be \(x\); then the price of gold is 10 times that, i.e. \(10x\).
Cost = quantity × price. Cost of copper \(= 7k \times x = 7kx\), and this is given as \(28000\) rupees.
So \(7kx = 28000\), which gives \(kx = 4000\).
Cost of gold \(= 4k \times 10x = 40kx\).
Substitute \(kx = 4000\): \(\text{gold cost} = 40 \times 4000 = 160000\) rupees.
Total cost of the bracelet = gold cost + copper cost \(= 160000 + 28000 = 188000\) rupees.
Key concept: keeping one combined unknown \(kx\) avoids solving for \(k\) and \(x\) separately. Hence the cost of the bracelet is Rs. 188000.
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