Question

on an astide with masked price Rs. 2000
a customes has choice between the sceesive
discounts of 20% - 20% and 10% and three
successive discounts of 40%.5% and 5%
how much can he save by choosing the
better offer ?​

Answer 1

AnswEr :

69.

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

On an articles with marked price Rs.2000 a customers has choice between the 3 successive discounts of 20% , 20% and 10% and other 3 successive discount of 40%, 5% and 5%.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

He save by choosing the better offer.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Formula use :

$\bf{\boxed{\sf{Selling\:price\:(S.P.)=M.P.\bigg[1-\frac{Discount\:(\%)}{100} \bigg]}}}}$

$\bf{\underline{\underline{\bf{According\:to\:the\:question\::}}}}}$

$\bf{\large{\pink{\underline{\underline{\tt{1_{st}\:Case\::}}}}}}$

$\mapsto\sf{S.P.=2000\bigg[1-\dfrac{20}{100} \times 1-\dfrac{20}{100} \times 1-\dfrac{10}{100} \bigg]}\\\\\\\mapsto\sf{S.P.=2000\bigg[\dfrac{100-20}{100} \times \dfrac{100-20}{100} \times \dfrac{100-10}{100} \bigg]}\\\\\\\mapsto\sf{S.P.=2000\bigg[\dfrac{8\cancel{0}}{10\cancel{0}} \times \dfrac{8\cancel{0}}{10\cancel{0}} \times \dfrac{9\cancel{0}}{10\cancel{0}} \bigg]}\\\\\\\mapsto\sf{S.P.=2000\bigg[\dfrac{8\times 8\times 9}{1000} \bigg]}$

$\mapsto\sf{S.P.=2\cancel{000}\times \dfrac{8\times 8\times 9}{\cancel{1000}} }\\\\\\\mapsto\sf{S.P.=Rs.(3\times 8\times 8\times 9)}\\\\\\\mapsto\sf{\red{S.P.=Rs.1152}}$

$\bf{\large{\pink{\underline{\underline{\tt{2_{nd}\:Case\::}}}}}}$

$\mapsto\sf{S.P.=2000\bigg[1-\dfrac{40}{100} \times 1-\dfrac{5}{100} \times 1-\dfrac{5}{100} \bigg]}\\\\\\\mapsto\sf{S.P.=2000\bigg[\dfrac{100-40}{100} \times \dfrac{100-5}{100} \times \dfrac{100-5}{100} \bigg]}\\\\\\\mapsto\sf{S.P.=2000\bigg[\dfrac{6\cancel{0}}{10\cancel{0}} \times \dfrac{95}{100} \times \dfrac{95}{100} \bigg]}\\\\\\\mapsto\sf{S.P.=2000\bigg[\dfrac{6\times 95\times 95}{100000} \bigg]}$

$\mapsto\sf{S.P.=2\cancel{000}\times \dfrac{6\times 95\times 95}{\cancel{1000}00} }\\\\\\\mapsto\sf{S.P.=\dfrac{2\times 6\times 95\times 95}{100}}\\\\\\\mapsto\sf{S.P.=\cancel{\dfrac{108300}{100} }}\\\\\\\mapsto\sf{\red{S.P.=Rs.1083}}$

Now;

Difference between the two offer, we get;

$\leadsto\sf{Difference=S.P.-S.P.}\\\\\leadsto\sf{Difference=Rs.1152-Rs.1083}\\\\\leadsto\sf{\red{Difference=Rs.69}}$

Thus;

$\underbrace{\sf{He\:saved\:by\:choosing\:the\:better\:offer=\:\pink{Rs.69}}}}$

Answer 2

Question:

on an astide with marked price Rs. 2000 a customes has choice between the sceesivediscounts of 20% - 20% and 10% and threesuccessive discounts of 40%.5% and 5%how much can he save by choosing thebetter offer ?

Answer:

when succes successive discount is 20%,20%,10%

$s.p = m.p(1 - \frac{discount}{100} ) \\ \\ where \: m.p = 2000 \\ \\ s.p = 2000(1 - \frac{20}{100} \times 1 - \frac{20}{100} \times 1 - \frac{10}{100} ) \\ \\ s.p = 2000( \frac{100 - 20}{100} \times \frac{100 - 20}{100} \times \frac{100 - 10}{100} ) \\ \\ s.p = 2000( \frac{80}{100} \times \frac{80}{100} \times \frac{90}{100} ) \\ \\ s.p = 2000(\frac{8 \times 8 \times 9}{1000} ) \\ \\ s.p =2 (8 \times 8 \times 9) \\ \\ s.p = 1152 \: rs....(1)$

When successive discount is 40%,5%,5%

$again \\ \\ s.p =2000 ( 1 - \frac{40}{100} \times 1 - \frac{5}{100} \times 1 - \frac{5}{100} ) \\ \\ s.p = 2000( \frac{100 - 40}{100} \times \frac{100 - 5}{100} \times \frac{100 - 5}{100} ) \\ \\ s.p = 2000( \frac{60}{100} \times \frac{95}{100} \times \frac{95}{100} ) \\ \\ s.p = 2000( \frac{6 \times 95 \times 95}{100000} ) \\ \\ s.p = \frac{2 \times 6 \times 95 \times 95}{100} \\ \\ s.p = \frac{108300}{100} \\ \\ s.p = 11083 \: rs....(1)$

subtract (1) and (2) we get,

=> 1152-1083

=>69

he saved Rs. 69 by choosing the best offer.