The Broken Coins

A man had three coins--a sovereign, a shilling, and a penny--and he found that exactly the same fraction of each coin had been broken away. Now, assuming that the original intrinsic value of these coins was the same as their nominal value--that is, that the sovereign was worth a pound, the shilling worth a shilling, and the penny worth a penny--what proportion of each coin has been lost if the value of the three remaining fragments is exactly one pound?

H. E. Dudeney, Amusements in Mathematics (1917) · No. 29