in this question v have to find duration,the kit has solved by finding irr first then finding duration using irr as discount rate. my question is why should we use irr and not couponrate i.e cost of debt
The IRR of the first bond is calculated so as to be able to calculate the market value of the second bond. (The IRR of the first bond is the gross redemption yield. The question says that it is the same for both bonds, and it is the gross redemption yield that (as always) determines the market value of the second bond).