Question

7. A person paid income tax at the rate of R%
for the first Rs 2 lakhs, and at the rate of
(R+10)% for income exceeding Rs 2 lakhs. If
the total tax paid is (R+5)% of the annual
income, then what is the annual income ?
1. Rs 2.5 lakhs
2. Rs 3.0 lakhs
3. Rs 4.0 lakhs
4. Rs 5.0 lakhs​

Answer 1

||✪✪ QUESTION ✪✪||

A person paid income tax at the rate of R%

for the first Rs 2 lakhs, and at the rate of

(R+10)% for income exceeding Rs 2 lakhs. If

the total tax paid is (R+5)% of the annual

income, then what is the annual income ?

1. Rs 2.5 lakhs

2. Rs 3.0 lakhs

3. Rs 4.0 lakhs

4. Rs 5.0 lakhs

( Good Question. )

|| ✰✰ ANSWER ✰✰ ||

Let The annual income is Rs.x .

As given Tax rate upto 2 lakhs is R% .

So,

→ Tax paid was = Rs.(2,00,000) * R/100 ----- Equation ❶

_______________

Now, Tax rate after 2 lakhs is (R+10%).

So,

→ Tax paid was = [(x - 200000) * (R+10)]/100 --- Equation ❷

________________

And, all over Tax rate was (R+5)% .

So,

→ All over Tax paid = [ x * (R+5) ] /100 --------- Equation ❸

__________________________

Adding Equation ❶ & ❷ Now, and putting Equal to Equation ❸ , we get,

☛ [ (2,00,000) * R/100 ] + [(x - 200000) * (R+10)]/100 = [ x * (R+5) ] /100

Denominator 100 will be cancel from both sides ,

☛ [ 200000R + ((x - 200000) * (R+10)) ] = x (R + 5)

☛ [ 200000R + xR + 10x - 200000R - 2000000 ] = xR + 5x

☛ 10x - 5x = 2000000

☛ 5x = 2000000

☛ x = 400000 = Rs. 4 lakhs (Option ❸ ).

Hence, the annual income is Rs 4.0 lakhs .

꧁________________________꧂

Answer 2

ANSWER :-

Let The annual income is Rs.x .

According to Question :-

=> [ (2,00,000) * R/100 ] + [(x - 200000) * (R+10)]/100 = [ x * (R+5) ] /100

=> [ 200000R + ((x - 200000) * (R+10)) ] = x (R + 5)

=> [ 200000R + xR + 10x - 200000R - 2000000 ] = xR + 5x

=> 10x - 5x = 2000000

=> 5x = 2000000

=> x = 400000 = Rs. 4 lakhs (Option 3)

Hence, the annual income is Rs 4.0 lakhs .