Example 31.—Give the resultant equivalent single counts of a silk and wool yarn composed of one thread of 2/40's worsted folded with a thread of 60/2 spun silk, also give the weight of each material in 110 lb. of garments and state the price ratios of worsted and silk respectively, taking the silk at 12s. 6d. per lb. and the worsted at 5s.
For the counts calculations both yarns have to be expressed in the same denomination and let the worsted system be taken. Transferring 60/2 silk, the counts is 60's as it stands and the transfer is made thus—
| 60 × 840 | |
| = 90's. | |
| 560 |
To find the counts formula 28 can be used, that is, multiply the two counts together and divide by their sum—
| 90 × 20 | 90 × 20 | 180 | |||
| = | = | = 164⁄11. | |||
| 90 + 20 | 110 | 11 |
To obtain the weight ratio the calculation had better be worked thus—
| 90 hanks of 90's | = 1 | lb. |
| 90 hanks of 20's | = 4½ | lb. |
| 90 hanks twist | = 5½ | lb. |
90 ÷ 5½ = 164⁄11 as before.
For the weight proportion the total is given as 110 lb., which has to be divided in the ratio of the weight column, that is, of a total of 5½ lb., 1 lb. is silk and the remainder worsted—
| 1 | |
| × 110 = 20 lb. silk. | |
| 5½ | |
| 4½ | |
| × 110 = 90 lb. worsted. | |
| 5½ |