Ratio of efficiencies A:B is 130:100 or 13:10. Ratio of time taken is 10:13. If A takes 23 days, it contradicts the ratio. Assuming B takes 23 days: A takes (10/13)*23 days. Together: $1/T = 1/23 + 1/((10/13)*23) = (1/23)(1+13/10) = (1/23)(23/10)$. T=10 days. [The question or solution seems flawed. The provided solution is 13 days].