UPSC CDS Math Ratio Proportion and Variation Questions

Let the weights of the diamonds be k, 2k, 3k and 4k.
Total weight of the diamond =k+2k+3k+4k=10k
Price of the original diamond
=λ(10k)2=₹100λk2
Total price of the four pieces of diamond
=λ[k2+(2k)2+(3k)2(4k)2]
=₹30λk2
Loss in total value of diamond
=100λk2−30λk2
=₹70λk2
∴70λk2=70000
⇒λk2=1000
Therefore, price of the original diamond =100×1000
=₹1,00,000