Consider the following statements:
I. Successive discounts of 10% and 20% are equal to a single discount of 30%.
II. Successive discounts of 25% and 20% are equal to a single discount of 40%.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only II
Successive discounts multiply: discounts of \(a\%\) and \(b\%\) equal a single discount of \(\left(a+b-\displaystyle\frac{ab}{100}\right)\%\).
I. Successive discounts of 10% and 20% are equal to a single discount of 30%. — Incorrect. The second discount is taken on the reduced price, so the single discount is 28%.
Price left \(=0.90\times0.80=0.72\) of the marked price
Single discount \(=1-0.72=0.28=28\%\)
II. Successive discounts of 25% and 20% are equal to a single discount of 40%. — Correct. The price left is 0.60 of the marked price.
Price left \(=0.75\times0.80=0.60\) of the marked price
Single discount \(=1-0.60=0.40=40\%\)