We investigate the possibility of explaining the enhancement in semileptonic decays of ${\bar{B}} → D^{(*)} τ {\bar{\nu }}$ B¯→D(∗)τν¯ , the anomalies induced by $b→ sμ ^+μ ^-$ b→sμ+μ- in ${\bar{B}}→ (K, K^*, ϕ )μ ^+μ ^-$ B¯→(K,K∗,ϕ)μ+μ- and violation of lepton universality in $R_K = \mathrm{Br}({\bar{B}}→ K μ ^+μ ^-)/\mathrm{Br}({\bar{B}}→ K e^+e^-)$ RK=Br(B¯→Kμ+μ-)/Br(B¯→Ke+e-) within the framework of R-parity violating MSSM. The exchange of down type right-handed squark coupled to quarks and leptons yields interactions which are similar to leptoquark induced interactions that have been proposed to explain the ${\bar{B}} → D^{(*)} τ {\bar{\nu }}$ B¯→D(∗)τν¯ by tree level interactions and $b→ s μ ^+μ ^-$ b→sμ+μ- anomalies by loop induced interactions, simultaneously. However, the Yukawa couplings in such theories have severe constraints from other rare processes in B and D decays. Although this interaction can provide a viable solution to the $R(D^{(*)})$ R(D(∗)) anomaly, we show that with the severe constraint from ${\bar{B}} → K ν {\bar{\nu }}$ B¯→Kνν¯ , it is impossible to solve the anomalies in the $b→ s μ ^+μ ^-$ b→sμ+μ- process simultaneously.