Question

The difference between a discount of 40% of Rs. 1000 and two successive discounts of 30% and 10% on the same amount is
A. 0
B. 20
C. 30
D. 40

Answer 1

Hint: We will first consider the given data. As we have to find the difference between a discount and two successive discounts. So, we will start by finding 40% of Rs. 1000 and then find the equivalent discount of successive discounts by using \[\left( {A + B - \dfrac{{A \times B}}{{100}}} \right)\% \]. After finding the value we will find the equivalent discount obtained of Rs. 1000. Then subtract the highest from the lowest to determine the difference between them.

Complete step by step answer:

The aim is to find the difference between a single discount and on the two successive discounts on the same amount.
We will start by finding the discount on 40% of Rs. 1000.
Thus, we get,
\[ \Rightarrow 40 \times \dfrac{{1000}}{{100}} = 400\]-------(1)
Now, we will find the equivalent discount of successive discounts given by \[A = 30\% \] and \[B = 10\% \] by using \[\left( {A + B - \dfrac{{A \times B}}{{100}}} \right)\% \].
Hence, we have,
\[ \Rightarrow \left( {30 + 10 - \dfrac{{30 \times 10}}{{100}}} \right) = 40 - 3 = 37\% \]
Now, as we obtained the equivalent discount also, so, we will now find the 37% discount on Rs. 1000.
Thus,
\[ \Rightarrow 37 \times \dfrac{{1000}}{{100}} = 370\]------(2)
Now, we will subtract the obtained values in equation (2) from equation (1)
\[ \Rightarrow 400 - 370 = 30\]
Hence, we can conclude that the difference between discounts is Rs. 30.

Note: Whenever we need to solve the statement like a% of Rs. B then we just have to multiply by \[\dfrac{B}{{100}}\]. For finding the equivalent discount on successive accounts we have to use the expression \[\left( {A + B - \dfrac{{A \times B}}{{100}}} \right)\% \] so, we need to remember this. We will let the one account as \[A\] and the other account as B in the successive accounts. The substitution of values in the formula should be done properly. Focus on the calculations done in the solution.