$3\mathrm{.}10$ The following information has been provided regarding a company that sells bicycles. The firm purchases goods already produced and sells them to consumers. The firm uses the weighted average method and a periodic inventory valuation system. The following information has been provided for the period April $20$X$6$:

The inventory balances available on $1$ April $20x6$ is $500$ units at R$260$ per unit and on $30$ April $206$ is $900$ units.

The following purchases occurred during April $20$X$6$:

$3$ April $20$X$6$: $500$ units at R$270$ per unit $($transportation costs were R$500)$

$15$ April $20$X$6$: $800$ units at R$300$ per unit $($transportation costs R$650)$

$28$ April $20$X$6$: $560$ units valued at R$150000.$

The following two returns occurred during the month:

$17$ April $20$X$6$: $60$ units valued at R$18000$

$29$ April $20$X$6$: $170$ units valued at R$20000.$

Required:

$($a$)$ Calculate the value of closing inventory on $30$ April $206.$

$($b$)$ The firm determined there were $1000$ bicycles sold during the month. Calculate if there has been any surplus or deficit during the month of April $20$X$6$