A man bought a bike for £20 and gave the bike dealer a cheque for £30 to pay for it. The bike dealer persuaded a shopkeeper to change the cheque for him and the buyer, having received his £10 change, rode off on the bike and was not seen again. Later, the cheque was found to be valueless and the bike dealer had to refund the shopkeeper the amount he had received. The bike dealer had bought the bike for £10. How much did the bike dealer lose altogether?
£20. £10 as change for the cheque and £10 for the bike originally.