Question

Represent three successive discounts of 10%,(25/3)% and (20/3)% by a single discount percentage.​

Answer 1

Answer:

Given:

The successive discounts are 8%, 15% and 12%.

Concept used:

Using the concept of percentage.

Calculation:

Let the initial value be 100.

Discounted value = (100 – 8)% of (100 – 15)% of (100 – 12)% of 100

⇒ Discounted value = 92% of 85% of 88% of 100

⇒ Discounted value = 92/100 × 85/100 × 88/100 × 100

⇒ Discounted value = 68.816

Equivalent discount = (100 – Discounted value)/Initial value × 100

⇒ Equivalent discount = (100 – 68.816)/100 × 100

⇒ Equivalent discount = 31.184%

∴ A single discount equivalent to three successive discounts is 31.184%.

Answer 2

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

Let assume that marked price of an article be Rs 100.

According to statement, three successive discounts of 10%, $\dfrac{25}{3}$% and $\dfrac{20}{3}$% is given on article.

We know,

Selling Price of an article if successive discounts of x %, y % and z % is applicable on marked price is given by

$\boxed{ \rm{ \:Selling \: Price = Marked \: Price\bigg(1 - \dfrac{x}{100} \bigg) \bigg(1 - \frac{y}{100} \bigg) \bigg(1 - \frac{z}{100}\bigg) \: }}$

So, on substituting the values, we get

$\bf \: Selling \: Price$

$\rm \: = \: 100\bigg(1 - \dfrac{10}{100} \bigg)\bigg(1 - \dfrac{25}{300} \bigg)\bigg(1 - \dfrac{20}{300} \bigg)$

$\rm \: = \: 100\bigg(1 - \dfrac{1}{10} \bigg)\bigg(1 - \dfrac{1}{12} \bigg)\bigg(1 - \dfrac{1}{15} \bigg)$

$\rm \: = \: 100\bigg(\dfrac{10 - 1}{10} \bigg)\bigg(\dfrac{12 - 1}{12} \bigg)\bigg(\dfrac{15 - 1}{15} \bigg)$

$\rm \: = \: 100\bigg(\dfrac{9}{10} \bigg)\bigg(\dfrac{11}{12} \bigg)\bigg(\dfrac{14}{15} \bigg)$

$\rm \: = \: 77$

$\rm\implies \:\bf \: Selling \: Price \: = \: Rs \: 77$

So,

$\bf\implies \:Single \: discount \: = \: (100 - 77)\% = 23\% \:$

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

Additional Information :-

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