Match List-I with List-II.
| List-I (Times taken by A and B alone) | List-II (Time taken together) | ||
|---|---|---|---|
| (A) | 6 days and 12 days | (I) | 12 days |
| (B) | 10 days and 15 days | (II) | 4 days |
| (C) | 20 days and 30 days | (III) | 20 days |
| (D) | 36 days and 45 days | (IV) | 6 days |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
If A and B alone take \(a\) and \(b\) days, together they take \(\displaystyle\frac{ab}{a+b}\) days.
(A) 6 days and 12 days — this matches (II) 4 days. \(\displaystyle\frac{6\times12}{6+12}=\displaystyle\frac{72}{18}=4\)
(B) 10 days and 15 days — this matches (IV) 6 days. \(\displaystyle\frac{10\times15}{10+15}=\displaystyle\frac{150}{25}=6\)
(C) 20 days and 30 days — this matches (I) 12 days. \(\displaystyle\frac{20\times30}{20+30}=\displaystyle\frac{600}{50}=12\)
(D) 36 days and 45 days — this matches (III) 20 days. \(\displaystyle\frac{36\times45}{36+45}=\displaystyle\frac{1620}{81}=20\)