We have, if V ml be the volume of 0.1MHCOONa be mixed to 50ml of 0.05M HCOOH,

[Molarity]= Total volume/Total milimole

In mixture [HCOONa]= (V+50)/(0.1×V)

[HCOOH]= (V+50)/(50×0.05)

As pH =−log(K a ) + log( [Acid]/[Salt)

∴ 4.0=3.70+log (V+50)/(2.5)/ (V+50)/ (0.1×V)

So v= approx. 50ml

Hope you understand this!