Tangency by hand

Three uncorrelated assets: a Nifty index fund (μ 12%, σ 15%), a mid-cap fund (14%, 20%), a short-duration debt fund (8%, 10%). Risk-free 6%. Compute the tangency weights and its Sharpe ratio. Show that with a diagonal covariance, the unnormalised tangency weight of each asset is its Sharpe ratio divided by its volatility.