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Hi experts,
Can you please help me with this question. Is there is any way to solve this question quickly. I used the plugin method. though, i got the right answer but it took me approx 3 min.
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Anthony, who lives in Zoolandia, pays 20% income tax on his earnings up to Z$30'000, 30% from Z$30'000 to Z$50'000 and 40% above Z$50'000. How much did he earn last year if he paid a 36% effective tax rate?

A) Z$210'000

B) Z$200'000

C) Z$190'000

D) Z$180'000

E) Z$160'000

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Total tax = tax 1 + tax 2 + tax 3
Total tax rate is 36% (Given as "effective tax rate")
Let total income be x

So:-

0.36(x) = 0.2(30k) + 0.3(50k-30k) + 0.4(x-50k)
0.36x = 6k + 6k + 0.4x - 20k
0.36x = 0.40x - 8k
-0.04x = -8000
4x = 800000
x = 200000
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Is it a fair way to select the middle value of 190,000 and then use option elimination or do you think the other options are too closely located and we may end up making a mistake ?

Actually that's what happened, lol !

Sometime algebra is better .. At least gives you a right answer :)

0.36*x = 12,000 + 0.4*(x-50,000)
x= 200,000.
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Anthony, who lives in Zoolandia, pays 20% income tax on his earnings up to Z$30'000, 30% from Z$30'000 to Z$50'000 and 40% above Z$50'000. How much did he earn last year if he paid a 36% effective tax rate?

A) Z$210'000

B) Z$200'000

C) Z$190'000

D) Z$180'000

E) Z$160'000

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Average of 20%, 30% and 40% is 36%.

We know that 20% was paid on 30k and 30% on 20k so their average will be 24% (using the scale method).

Average of 24% and 40% is 36% so distance of 36 from 24 : distance of 36 from 40 is 3:1. This means that weights given to 24% and 40% are in the ratio 1:3. Since he paid overall 24% on 50k, he paid 40% on 150k.

Overall amount is 50k + 150k = 200k

Answer (B)

I have discussed weighted averages with 3 quantities here: https://youtu.be/Ye8IEJ_lz6E
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