Math, asked by 2001harpreetkaur, 8 months ago

The Income-tax on an individual income varies as the square

of the excess of the individual’s yearly income over Rs.6,000/-

. The tax on yearly income of Rs.10,000/- is Rs.640/-. Find the

tax on yearly income of Rs.12,000/-.​

Answers

Answered by pulakmath007
51

SOLUTION

GIVEN

  • The Income-tax on an individual income varies as the square of the excess of the individual’s yearly income over Rs.6,000/-

  • The tax on yearly income of Rs.10,000 is Rs.640

TO DETERMINE

The tax on yearly income of Rs. 12,000

EVALUATION

Let total income = Rs x and tax payable = Rs T

So by the given condition

 \sf{T \propto \:  {(x - 6000)}^{2}  }

 \implies \sf{T  = k \:  {(x - 6000)}^{2}  } \:  \: ........(1)

Where k is a non zero constant

Now T = 640 when x = 10000

From Equation 1 we get

 \implies \sf{640  = k \:  {(10000 - 6000)}^{2}  }

  \displaystyle  \implies \sf{k =  \frac{640}{ {(4000)}^{2} }  }

Now we to find T when x = 12000

From Equation (1) we get

  \displaystyle  \implies \sf{T = k{(12000 - 6000)}^{2}  }

  \displaystyle  \implies \sf{T = \frac{640}{ {(4000)}^{2} } \times   {( 6000)}^{2}    }

  \displaystyle  \implies \sf{T = \frac{640 \times 36}{ 16 }  }

  \displaystyle  \implies \sf{T = 40 \times  36 }

  \displaystyle  \implies \sf{T = 1440  }

FINAL ANSWER

The tax on yearly income of Rs. 12,000 is

Rs. 1440

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