We present a BVI optical photometric study of the old open cluster Ruprecht 6 using the data obtained with the SMARTS 1.0 m telescope at the CTIO, Chile. Its color-magnitude diagrams show the clear existence of the main-sequence stars, of which turn-off point is located around V ~ 18.45 mag and B-V ~ 0.85 mag. Three red clump (RC) stars are identified at V = 16.00 mag, I = 14.41 mag and B-V = 1.35 mag. From the mean Ks-band magnitude of RC stars (Ks=12.39 +- 0.21 mag) in Ruprecht 6 from 2MASS photometry and the known absolute magnitudes of the RC stars (M_Ks = -1.595 +- 0.025 mag), we obtain the distance modulus to Ruprecht 6 (m-M)_0 = 13.84 +- 0.21 mag (d=5.86 +- 0.60 kpc). From the (J-K_s) and (B-V) colors of the RC stars, comparison of the (B-V) and (V-I) colors of the bright stars in Ruprecht 6 with those of the intrinsic colors of dwarf and giant stars, and the PARSEC isochrone fittings, we derive the reddening values of E(B-V) = 0.42 mag and E(V-I) = 0.60 mag. Using the PARSEC isochrone fittings onto the color-magnitude diagrams, we estimate the age and metallicity to be: log (t) =9.50 +- 0.10 (t =3.16 +- 0.82 Gyr) and [Fe/H] = -0.42 +- 0.04 dex. We present the Galactocentric radial metallicity gradient analysis for old (age > 1 Gyr) open clusters of Dias et al. catalog, which likely follow a single relation of [Fe/H] =(-0.034 +- 0.007) R_GC + (0.190 +- 0.080) (rms = 0.201) for the whole radial range or dual relation of [Fe/H] =(-0.077 +- 0.017) R_GC + (0.609 +- 0.161) (rms = 0.152) and constant ([Fe/H] ~ -0.3 dex) value, inside and outside of R_GC ~ 12 kpc, respectively. The metallicity and Galactocentric radius (13.28 +- 0.54 kpc) of Ruprecht 6 obtained in this study seem to be consistent with both of the relations.
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