PMstandard costing and variance

Q Ltd operates a system of standard costing and in respect of one of its products which is manufactured within a single cost centre, the following information is given. For one unit of product the standard material input is 16 litres at a standard price of £2.50 per litre. The standard wage rate is £5 per hour and 6 hours are allowed in which to produce one unit. Fixed production overhead is absorbed at the rate of 120% of direct wages cost. During the last four-week accounting period: The material price variance was extracted on purchase and the actual price paid was £2.45 per litre. Total direct wages cost was £121,500. Fixed production overhead incurred was £150,000. Variances Favourable Adverse £ £ Direct material price 8,000 Direct material usage 6,000 Direct labour rate 4,500 Direct labour efficiency 3,600 Fixed production overhead expenditure 6,000 You are required to calculate for the four-week period: (i) budgeted output in units; (ii) number of litres purchased; (iii) number of litres used above standard allowed; (iv) actual units produced; Workings (a) (i) Budget overhead cost = £150,000 – £6,000 = £144,000 Budget cost/unit = 120% (6 hrs × £5) = £36 Budgeted units = £36 £144,000 = 4,000 (ii) Material price variance = £8,000 (F) Price variance/litre = £0.05 (F) Quantity purchased = 05.0£ ,8£ 000 = 160,000 litres (iii) Usage variance = £6,000 (A) Standard price = £2.50/litre Excess usage = 50.2£ ,6£ 000 = 2,400 litres (iv) Actual wage cost = £121,500 Total wage variance = £900 (A) ––––––– Standard cost = £120,600 ––––––– Standard cost/unit = 6 hours @ £5 = £30 Actual output = £30 £120,600 = 4,020 units problem I understand how the 4020 actual units have been calculated, however if inserted to calculate a variance, say direct material usage variance it will not give -6000 as per the question. material usage variance=((16*4020)-160000)*2.5= -239200 while the question says its -6000 Another way to calculate the variance is using the material usage variance material usage variance= (160000- std qty)*2.5 -6000=(160000-std qty)*2.5 std quantity= 157600 litres no. of units= 157600/16=9850 units. However if 9850 units is used then labour rate variance will not be -4500 either way, the units calculated are different and non fit into each other. Please i hope you can assist me understand if im going wrong anywhere. thank you.