in 2003 brijesh paid a tax of 20% of his salary. in 2004 his salary increased by 93×3/4 % and the tax scheme changed. under the new tax scheme he had to pay a fixed sum of rs.1000 and an additional 20% on the amount above rs 10000. his salary in 2004 was more than rs 10000 and he paid a tax of rs 500 more than what he paid in 2003. what is his salary in 2004

Question

in 2003 brijesh paid a tax of 20% of his salary. in 2004 his salary increased  by 93×3/4 % and the tax scheme changed. under the new tax scheme he had to pay a fixed sum of rs.1000 and an additional 20% on the amount above rs 10000. his salary in 2004 was more than rs 10000 and he paid a tax of rs 500 more than what he paid in 2003. what is his salary in 2004
Please help me out

Dr_HULK · Accepted Answer

let in 2003, his salary was x so paid tax in 2003 was 20x/100
in 2004 salary was increased by 93 3/4%=93.75% So salary was increased 93.75x/100 and
total salary in 2004 was x+ (93.75x/100)
So additional amount is [x+ (93.75x/100)]-10000
additional tax[{x+ (93.75x/100)}-10000] * 20/100
total tax in 2004 was 1000+ [{x+ (93.75x/100)}-10000] * 20/100

So now tax in 2004-tax in 2003=500
so 1000+ [{x+ (93.75x/100)}-10000] * 20/100 - 20x/100=500
after simplification above expression
=>100000+[x+(93.75x/100)-10000]*20 - 20x =50000
=>50000+20x+(93.75x/5)-200000-20x=0
=>93.75x/5=150000
=>x=150000*5/93.75
=>x=8000
So his salary in 2004 was x+ (93.75x/100)
=>8000+(93.75*8000/100)=Rs 15500
So his salary in 2004 was Rs 15500
Proof:
So his salary in 2003 was Rs 8000
So tax in 2003 was 8000*20/100=Rs 1600
in 2004, salary was increased by 93.75% so total salary was 8000+(8000*93.75/100)=8000+7500=Rs 15500
so now tax was 1000(fix)+ 20% additional above salary of 10000
=>tax in 2004 was 1000+20% of 5500
so tax in 2004, was 1000+1100=Rs 2100
so the difference in tax was 2100-1600=Rs 500