Question

A piece of land is marked at Rs. 5,00,000. The dealer allows three successive discounts of 7 1/2 % , 6 % and 4% on it. What is the net selling Price?​

Answer 1

$\bf \underline{Given} : \sf \implies Marked \: price \: of \: a \: land = Rs. \: 5,00,000$

$\sf \: First \: discount = 7 \: \dfrac{1}{2} \: \% \: of \: Rs. \: 500000$

$\sf \implies \dfrac{15}{2 \times 100} \: \times 500000$

$\sf \implies \dfrac{15}{2 } \: \times 5000 = Rs. \: 37500$

$\sf Price \: after \: first \: discount = Rs. \: (500000-37500)$

$\sf Price \: after \: first \: discount = Rs. \:462500$

$\sf Second \: discount = 6 \: \% \: of \: Rs. \: 462500$

$\sf \implies \dfrac{6}{ 100} \: \times Rs. \: 462500$

$\sf \implies \dfrac{6}{ 1} \: \times 4625 \: = Rs. \: 27750$

$\sf Price \: after \: second \: discount = Rs. \: (462500-27750)$

$\sf Price \: after \: second \: discount = Rs. \: 434750$

$\sf Third \: discount = 4 \: \% \: of \: Rs. \: 434750$

$\sf \implies \dfrac{4}{ 100} \: \times Rs. \: 434750$

$\sf \implies \dfrac{4}{ 10} \: \times 43475= Rs. \: 17390$

$\sf Price \: after \: third \: discount = Rs. \: (434750-17390)$

$\sf Price \: after \: third \: discount = Rs. 417360$

$\underline{ \boxed{ \red{ \sf Therefore, Net \: price = Rs. \: 417360 }}}$

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$\bf \underline{Alternative \: Method }:$

$\sf \: Here, d_1 = 7 \: \dfrac{1}{2} = \dfrac{15}{2} \: \% \: , \: d_2 = 6 \: \% \: and \: d_3 = 4 \: \%$

$\sf Also, Marked \: price = Rs. \: 5,00,000$

$\sf Net \: price = \bigg(1 - \dfrac{d_ 1}{100} \bigg)\bigg(1 - \dfrac{d _ 2}{100} \bigg)\bigg(1 - \dfrac{d_ 3}{100} \bigg) \times \: Marked \: price$

$\sf \implies \bigg(1 - \dfrac{15}{2 \times 100} \bigg)\bigg(1 - \dfrac{6}{100} \bigg)\bigg(1 - \dfrac{4}{100} \bigg) \times Rs. \: 5,00,000$

$\sf \implies \dfrac{185}{200} \times \dfrac{94}{100} \times \dfrac{96}{100} \times 5,00,000$

$\underline{ \boxed{ \red{ \sf Therefore, Net \: price = Rs. \: 417360 }}}$