Comments on: A Tale of Two Tai Tais http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Wed, 24 Apr 2013 20:25:50 +0000 hourly 1 By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais#comment-38154 Miss Loi Sat, 10 Jul 2010 15:18:18 +0000 http://www.exampaper.com.sg/?p=1047#comment-38154 Ha! Just caught this comment ... As mentioned, this question is a little atypical so you won't discover any clues in Discovering Mathematics (pun not intended). Though the process of obtaining the in this case is admittedly a wee bit involved, the essence of solving this type of local <a href="/tag/taxation" rel="nofollow">taxation</a> problem (where we're shown our mighty IRAS tax table) is basically the same i.e. <span class="highlight">find which <em>row</em> does the <strong>chargeable</strong> income falls into</span>. As <span class="highlight">chargeable income = total income − reliefs</span>, we first calculate the reliefs of each <i>Tai Tai</i>'s husband <i>Tai Tai</i> <var>A</var>'s husband's total reliefs <span style="color:#DE7C81;">(read through the paras in red)</span> = $1000 (personal) + $2000 (Spouse) + 2 × $4500 (Parents not staying - ok let's assume her husband is a filial only child with both parents still alive) = $12000 <i>Tai Tai</i> <var>B</var>'s husband's total reliefs <span style="color:#77B42D;">(read through the paras in green)</span> = $1000 (personal) + $2000 (Spouse) + 2 × $7000 (Both parents staying with them) + 2 × $4000 (two kids) + $3000 (NSMan) = $28000 Now we don't know how much they earn, but we're given their tax payable as a % of their total income. To find out <em>which row</em> of the table they belong to, we can deduce from the table the <em>maximum</em> % of total income they are taxable at each row: <table> <tr> <th style="text-align:left;line-height:1;">Chargeable Income</th> <th style="text-align:left;line-height:1;">Rate (%)</th> <th style="text-align:left;line-height:1;">Max Tax Payable ($)</th> <th style="text-align:left;line-height:1;">Max % of <var>A</var>'s total income<br/>=max tax payable/(max chargeable income+ relief ($12000))</th> <th style="text-align:left;line-height:1;">Max % of <var>B</var>'s total income<br/>=max tax payable/(max chargeable income+relief ($28000))</th> </tr> <tr> <td>≤ $20,000</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> </tr> <tr> <td>≤ $30,000</td> <td>3.50</td> <td>350</td> <td>0.833</td> <td>0.603</td> </tr> <tr> <td>≤ $40,000</td> <td>5.50</td> <td>900</td> <td>1.731</td> <td>1.324</td> </tr> <tr> <td>≤ $80,000</td> <td>8.50</td> <td>4300</td> <td>4.674</td> <td>3.981</td> </tr> <tr> <td style="background-color:red;color:white;">≤ $160,000</td> <td style="background-color:red;color:white;">10.40</td> <td style="background-color:red;color:white;">15500</td> <td style="background-color:red;color:white;">9.012</td> <td style="background-color:red;color:white;">8.245</td> </tr> <tr> <td>≤ $320,000</td> <td>17</td> <td>42700</td> <td>12.86</td> <td>12.27</td> </tr> </table> So from their given percentages of 6% and 4% we can see from the table above that their total <em>chargeable</em> income is somewhere between $80000 and $160000. ⇒ Tax that each of them have to pay (<var>t</var>) = $4300 (for the first $80000) + <span class="highlight">14% of the part of the next $80000 (= total chargeable income (<var>i</var>) − $80000)</span> And since we know that [pmath]t_A/{i_A+$12000} = 6%[/pmath] and [pmath]t_B/{i_B+$28000} = 4%[/pmath] Can you solve for the unknowns and see whose husband actually has a higher <em>total</em> income? ;) Ha! Just caught this comment ...

As mentioned, this question is a little atypical so you won't discover any clues in Discovering Mathematics (pun not intended).

Though the process of obtaining the in this case is admittedly a wee bit involved, the essence of solving this type of local taxation problem (where we're shown our mighty IRAS tax table) is basically the same i.e. find which row does the chargeable income falls into.

As chargeable income = total income − reliefs, we first calculate the reliefs of each Tai Tai's husband

Tai Tai A's husband's total reliefs (read through the paras in red)
= $1000 (personal) + $2000 (Spouse) + 2 × $4500 (Parents not staying - ok let's assume her husband is a filial only child with both parents still alive)
= $12000

Tai Tai B's husband's total reliefs (read through the paras in green)
= $1000 (personal) + $2000 (Spouse) + 2 × $7000 (Both parents staying with them) + 2 × $4000 (two kids) + $3000 (NSMan)
= $28000

Now we don't know how much they earn, but we're given their tax payable as a % of their total income. To find out which row of the table they belong to, we can deduce from the table the maximum % of total income they are taxable at each row:

Chargeable Income Rate (%) Max Tax Payable ($) Max % of A's total income
=max tax payable/(max chargeable income+ relief ($12000))		 Max % of B's total income
=max tax payable/(max chargeable income+relief ($28000))
≤ $20,000 0 0 0 0
≤ $30,000 3.50 350 0.833 0.603
≤ $40,000 5.50 900 1.731 1.324
≤ $80,000 8.50 4300 4.674 3.981
≤ $160,000 10.40 15500 9.012 8.245
≤ $320,000 17 42700 12.86 12.27

So from their given percentages of 6% and 4% we can see from the table above that their total chargeable income is somewhere between $80000 and $160000.

⇒ Tax that each of them have to pay (t)
= $4300 (for the first $80000) + 14% of the part of the next $80000 (= total chargeable income (i) − $80000)

And since we know that
t_A/{i_A+$12000} = 6% and
t_B/{i_B+$28000} = 4%

Can you solve for the unknowns and see whose husband actually has a higher total income? ;)

]]> By: qwerty1106 http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais#comment-38145 qwerty1106 Sat, 03 Jul 2010 14:13:02 +0000 http://www.exampaper.com.sg/?p=1047#comment-38145 Hey the condo is sparkling not spanking. Are you sure you can do this question? think about 45min le(include referencing to Discovering Mathematics 4B) and i cant even know how to start!!! need to do this le:orz and burn more joss sticks(or rather learn this topic 1st) Hey the condo is sparkling not spanking.
Are you sure you can do this question? think about 45min le(include referencing to Discovering Mathematics 4B) and i cant even know how to start!!! need to do this le:orz and burn more joss sticks(or rather learn this topic 1st)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais#comment-36987 Miss Loi Wed, 14 Apr 2010 06:09:27 +0000 http://www.exampaper.com.sg/?p=1047#comment-36987 <span class="topsy_trackback_comment"><span class="topsy_twitter_username"><span class="topsy_trackback_content">A Tale of Two Tai Tais: http://bit.ly/a0QLdF</span></span> A Tale of Two Tai Tais: http://bit.ly/a0QLdF

]]> By: Miss Loi http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais#comment-36991 Miss Loi Wed, 14 Apr 2010 06:08:28 +0000 http://www.exampaper.com.sg/?p=1047#comment-36991 <span class="topsy_trackback_comment"><span class="topsy_twitter_username"><span class="topsy_trackback_content">http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais</span></span> http://www.exampaper.com.sg/questions/e-maths/a-tale-of-two-tai-tais

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