Question

9. Which is more favourable to the seller and by how much 800 with 20% discount or the same
amount with successive discounts of 12% and 10%?

Answer 1

Question :-

Which is more favourable to the seller and by how much?

800 with 20% discount or the same amount with

successive discounts of 12% and 10%?

$\large\underline{\sf{Solution-}}$

Case :- 1

Marked Price = 800

Discount % = 20 %

We know,

$\boxed{\rm{Selling \: Price = \dfrac{(100 - Discount\%) \times Marked \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 - 20) \times 800}{100}$

$\rm \: Selling \: Price = 80 \times 8$

$\rm\implies \:Selling \: Price \: = \: 640$

Case - 2

Marked Price = 800

Successive discounts = 12 % and 10 %

We know,

Selling Price when successive discounts of x % and y % is given on Marked Price is

$\boxed{\rm{  \:Selling \: Price = \frac{(100 - x\%)(100 - y\%) \times Marked \: Price}{10000} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 - 12)(100 - 10) \times 800}{10000}$

$\rm \: Selling \: Price = \dfrac{88 \times 90 \times 8}{100}$

$\rm \: Selling \: Price = \dfrac{88 \times 9 \times 8}{10}$

$\rm\implies \:Selling \: Price \: = \: 633.60$

So, Selling Price in case 2 < Selling Price in case 1.

So, Seller prefer first case. Discount of 20 % on 800

Now, Difference in Selling Price = 640 - 633.60 = 6. 40

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$