Match List-I with List-II.
| List-I (Successive changes) | List-II (Net change) | ||
|---|---|---|---|
| (A) | An increase of 20% followed by an increase of 10% | (I) | 19% decrease |
| (B) | An increase of 25% followed by a decrease of 20% | (II) | 32% increase |
| (C) | A decrease of 10% followed by a decrease of 10% | (III) | No change |
| (D) | An increase of 50% followed by a decrease of 40% | (IV) | 10% decrease |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
Two successive changes of \(a\%\) and \(b\%\) give a net change of \(\left(a+b+\displaystyle\frac{ab}{100}\right)\%\), a decrease being taken as negative.
(A) An increase of 20% followed by an increase of 10% — this matches (II) 32% increase. \(20+10+\displaystyle\frac{20\times10}{100}=30+2=32\)
(B) An increase of 25% followed by a decrease of 20% — this matches (III) No change. \(25-20+\displaystyle\frac{25\times(-20)}{100}=5-5=0\)
(C) A decrease of 10% followed by a decrease of 10% — this matches (I) 19% decrease. \(-10-10+\displaystyle\frac{(-10)\times(-10)}{100}=-20+1=-19\)
(D) An increase of 50% followed by a decrease of 40% — this matches (IV) 10% decrease. \(50-40+\displaystyle\frac{50\times(-40)}{100}=10-20=-10\)