A grain merchant found that 8% of a consignment was spoilt by damp, and 5% of what remained was eaten by rodents. If 8,740 kg was finally fit for sale, what was the weight of the consignment he received?

If the consignment weighed $W$ kg, then $Wx0.92\times 0.95=8740$. Since $0.92\times 0.95=0.874,W=8740/0.874=10,000$ kg. Check: 10000 -> 9200 after the damp -> 8740 after the rodents. 9,500 kg divides by 0.92 alone and 9,200 kg by 0.95 alone, each undoing only one stage. 10,046 kg adds the two cuts into a single 13% (8740/0.87) - the true survival factor is 87.4%, not 87%.