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)