Question

After successive discounts of 20% and 5% have been given, the net price of a commodity is Rs.456. Calculate (i) list price and (ii) A single discount payment which is equivalent to the successive discounts of 20% and 5%.

Answer 1

Hint: Assume the list price as ‘x’. First find the price after 20% discount is given by subtracting x from 20% of x. Now, find 5% discount on this new price calculated and equate that equal to 456 to get the value of x. For second part of the question, assume the equivalent discount as ‘d%’. Find the net price after a discount of d% on x and equate that equal to 456 to get the value of d.

Complete step by step answer:
Let us assume the list price as ‘x’. We have been given that there are two successive discounts of 20% and 5%. That means, first we have to consider a discount of 20% and calculate the price applicable, then on this new price we have to consider a 5% discount. So, we have,
(i) Price of commodity after 20% discount on x.
\[\Rightarrow x-20\%\]of x
\[\begin{align}
  & \Rightarrow x-\dfrac{20}{100}\times x \\
 & \Rightarrow x-\dfrac{x}{5} \\
 & \Rightarrow \dfrac{4x}{5} \\
\end{align}\]
Now, we have to consider a 5% discount on \[\dfrac{4x}{5}\]. Therefore, price of commodity after 5% discount on \[\dfrac{4x}{5}\],
\[\Rightarrow \dfrac{4x}{5}-5\%\] of \[\dfrac{4x}{5}\]
\[\begin{align}
  & \Rightarrow \dfrac{4x}{5}-\dfrac{5}{100}\times \dfrac{4x}{5} \\
 & \Rightarrow \dfrac{4x}{5}\left( 1-\dfrac{5}{100} \right) \\
\end{align}\]
It is given that this price is equal to 456.
\[\begin{align}
  & \Rightarrow \dfrac{4x}{5}\left( 1-\dfrac{5}{100} \right)=456 \\
 & \Rightarrow \dfrac{4x}{5}\left( 1-\dfrac{1}{20} \right)=456 \\
 & \Rightarrow \dfrac{4x}{5}\times \dfrac{19}{20}=456 \\
 & \Rightarrow x=\dfrac{456\times 20\times 5}{19\times 4} \\
 & \Rightarrow x=600 \\
\end{align}\]
Therefore, the list price is Rs.600.
(ii) Now let us assume the single discount as d% which is equivalent to successive discounts of 20% and 5%.
\[\Rightarrow \] Net price after d% discount = net price after 20% and 5% discount.
\[\Rightarrow \] x – d% of x = 456
\[\Rightarrow x-\dfrac{d}{100}\times x=456\]
Substituting x = 600, we get,
\[\begin{align}
  & \Rightarrow 600-\dfrac{d}{100}\times 600=456 \\
 & \Rightarrow 600-6d=456 \\
 & \Rightarrow 6d=600-456 \\
 & \Rightarrow 6d=144 \\
 & \Rightarrow d=24 \\
\end{align}\]
Hence, the equivalent discount is 24%.

Note: One must note that after a discount of 20% we do not have to calculate a 5% discount on the initial price but we have to calculate one the new discounted price and that is what the term successive discount signifies. Now, in the second part, since the equivalent discount d% is on list price, so we have calculated it on x = 600.