6 men or 7 women can do a job in 11 days. 6 men work for 10 days and leave.…

Efficiency-ratio method for work problems: if two different groups can each finish the same job on their own, the total work is one fixed quantity that can be expressed in either group's worker-days. Equating these two expressions gives the conversion ratio between one worker's daily output and the other's, and that ratio converts any partial work finished by one group into an equivalent amount for the other group, letting the remaining work and the required number of workers be calculated in either group's units.

1. Total work in man-days: 6 men finish the job in 11 days, so total work = 6 x 11 = 66 man-days.

2. Total work in woman-days: 7 women finish the same job in 11 days, so total work = 7 x 11 = 77 woman-days.

3. Conversion ratio: since 66 man-days = 77 woman-days for the identical job, 1 man-day = 77/66 woman-days = 7/6 woman-days.

4. Work done by the men: 6 men work for 10 days, completing 6 x 10 = 60 man-days, equivalent to 60 x 7/6 = 70 woman-days.

5. Remaining work: total work minus work done = 77 minus 70 = 7 woman-days.

6. Women required: the remaining 7 woman-days must be finished in 7 days, so women needed = 7 divided by 7 = 1.

Cross-check using work fractions: in 10 days, the 6 men complete 10/11 of the job (since they need 11 days for the whole job), leaving 1/11 of the job. One-eleventh of the total 77 woman-days is 77/11 = 7 woman-days, and finishing 7 woman-days of work in 7 days again needs 7/7 = 1 woman, confirming the same figure.

So exactly 1 woman is required to complete the remaining work in 7 days.