Usage variance example

Sometimes there is expected loss in the production process. Coope and Sorcerer Co make product T42 in a continuous process, for which standard and actual quantities in month 10 were as follows. Qty-----Std$/kg - value---Quantity kg -- actual price/kg--std cost of actual usg Material P 40000 --- 2.50 --100,000--34000-----------2.50------------------85000 Material Q 20000--- 4.00 ---80000---- 22000 ---------4.00 --------------- 88000 total---------60000-------------180000---- 56000------------------------------173000 Losses occur at an even rate during the processing operations and are expected to be 10% of materials input. So budgeted output for the month was 54000 of t42 (=60,000 * 90%). Actual output during the month was 51,300 kg of T42. Req = calculate the usage, mix and yield variance. Solution standard usage for actual output of 51,300 kg Kg Material P 38000 (51300/54000) * 40000 = 38000kg Material Q 19000 (51300/54000) * 20000 = 19000 kg 57000 Is there an alternative “easy” way of arriving to the above figures (38000 and 19000) ? (please note the above working is part of the solution for usage variances)