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
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
Well, well, well! It seems like Brijesh was trying to outsmart the tax system, but it caught up with him!
Let's break down the information given to solve this puzzle.
In 2003, Brijesh paid 20% of his salary in taxes. So, if we let his salary in 2003 be "x," the tax paid in 2003 would be 0.20x.
In 2004, Brijesh's salary increased by 93 × 3/4%. Let's calculate that! 93 × 3/4 equals 69.75.
So, his salary in 2004 was 69.75% higher than his 2003 salary. Let's represent his 2004 salary as "y," then we can write the equation y = x + 0.6975x.
Under the new tax scheme, he had to pay a fixed sum of Rs. 1000 and an additional 20% on the amount above Rs 10,000. So, his total tax paid in 2004 can be represented as 1000 + 0.20(y - 10000).
Now, the question says that he paid Rs 500 more in taxes in 2004 than he did in 2003. So we can set up another equation: 1000 + 0.20(y - 10000) = 0.20x + 500.
Alright, time to crunch those numbers! Let's simplify that equation:
1000 + 0.20y - 2000 = 0.20x + 500.
0.20y - 1000 = 0.20x + 500.
0.20y = 0.20x + 1500.
Divide everything by 0.20:
y = x + 7500.
Now we have a system of equations. We can substitute for y in the second equation:
x + 7500 = x + 0.6975x.
Simplify that equation:
7500 = 1.6975x.
Divide both sides by 1.6975:
x ≈ 4414.93.
So Brijesh's salary in 2003 was approximately Rs. 4414.93.
To find his salary in 2004, let's substitute this value into our equation for y:
y = 4414.93 + 7500.
y ≈ 11914.93.
Therefore, Brijesh's salary in 2004 was approximately Rs. 11,914.93.
Well, it seems like Brijesh had quite the jump in salary in 2004. I hope his funny bone is strong because he'll need it to cope with those taxes!
To find Brijesh's salary in 2004, we can start by setting up equations based on the given information.
Let's assume Brijesh's salary in 2003 was "x" rs.
In 2003, Brijesh paid a tax of 20% of his salary, which means he paid 0.2x rs in taxes.
In 2004, Brijesh's salary increased by 93×3/4 %, which is (93 * 3/4) / 100 = 69.75%. So, his salary in 2004 became (x + (69.75/100) * x) rs.
Under the new tax scheme, Brijesh had to pay a fixed sum of Rs. 1000 and an additional 20% on the amount above Rs. 10,000. Therefore, his total tax in 2004 was calculated as follows:
Tax = Rs. 1000 + (20/100) * (salary in 2004 - Rs. 10,000)
We know that Brijesh paid Rs. 500 more in taxes in 2004 than in 2003. So, we can set up the equation:
Tax in 2004 - Tax in 2003 = Rs. 500
Let's substitute the values we know into the equation:
(Rs. 1000 + (20/100) * (salary in 2004 - Rs. 10,000)) - 0.2x = Rs. 500
Simplifying the equation:
1000 + (0.2 * (salary in 2004 - 10,000)) - 0.2x = 500
Now, let's solve this equation step-by-step to find Brijesh's salary in 2004.
1. Subtract 500 from both sides:
1000 + (0.2 * (salary in 2004 - 10,000)) - 0.2x - 500 = 0
2. Combine like terms:
500 + (0.2 * (salary in 2004 - 10,000)) - 0.2x = 0
3. Simplify further:
0.2 * (salary in 2004 - 10,000) - 0.2x = -500
4. Divide all terms by 0.2:
salary in 2004 - 10,000 - x = -2500
5. Move x to the left side:
salary in 2004 - x = 10,000 - 2500
6. Simplify:
salary in 2004 - x = 7,500
7. Add x to both sides:
salary in 2004 = 7,500 + x
Therefore, the salary of Brijesh in 2004 would be 7,500 + x rs.
To solve this problem, let's start by finding out Brijesh's salary in 2003.
Let's assume his salary in 2003 was 'x'.
According to the given information, Brijesh paid a tax of 20% of his salary in 2003. So, the tax he paid in 2003 would be 20% of 'x', which is 0.2x.
Now, let's move on to find his salary in 2004.
The problem states that his salary in 2004 increased by 93×3/4 %.
This can be calculated as follows:
93×3/4 % = (93/100) × (3/4) = 279/400
So, his salary in 2004 would be (x + 279/400x).
Now, let's calculate the tax paid in 2004 using the new tax scheme.
According to the new tax scheme, Brijesh has to pay a fixed sum of Rs. 1000 and an additional 20% on the amount above Rs. 10,000.
So, the tax paid in 2004 would be 1000 + 20% of (salary in 2004 - 10,000).
Given that he paid a tax of Rs. 500 more in 2004 compared to 2003, we can write the equation as:
(1000 + 20% of (salary in 2004 - 10,000)) - (0.2x) = 0.2x + 500
Simplifying the equation further, we get:
1000 + 20% of (x + 279/400x - 10,000) - 0.2x = 0.2x + 500
1000 + (x + 279/400x - 10,000) × 0.2 - 0.2x = 0.2x + 500
1000 + 0.2x + 55.8/200x - 2000 + 0.2x = 0.2x + 500
Simplifying further, we get:
0.4x + 55.8/200x + 0.2x = 2500
Multiplying the entire equation by 200 to eliminate the denominator, we get:
80x + 55.8x + 40x = 500,000
175.8x = 500,000
x = 500,000 / 175.8
x ≈ 2840.22
Therefore, Brijesh's salary in 2004 would be (x + 279/400x):
Salary in 2004 = 2840.22 + 279/400 × 2840.22
Finally, calculating the value, we find that Brijesh's salary in 2004 would be approximately Rs. 4,791.