Question

Match List-l with List-ll

List I		List II
A.	Duplicate of ratio 2: 7	I.	25:30
B.	Compound ratio of 2: 7, 5:3 and 4:7	II.	4:49
C.	Ratio of 2: 7 is same as	III.	40:147
D.	Ratio of 5: 6 is same as	IV.	4:14

Choose the correct answer from the options given below:

• (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
• (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
• (A) - (IV), (B) (I), (C) - (II), (D) - (III)
• (A) - (I), (B) - (III), (C) - (IV), (D) - (II)

Answer 1

The Correct Option is B

To solve this problem, we need to match the entries in List I with the corresponding entries in List II by understanding the definition of each term.

1. Duplicate of a Ratio: The duplicate ratio of any given ratio \(a:b\) is \(a^2:b^2\).
   For the ratio 2:7, the duplicate ratio is:  
   \((2^2):(7^2) = 4:49\). 
   Thus, Duplicate of ratio 2:7 matches with II. 4:49.
2. Compound Ratio: The compound ratio of multiple ratios is found by multiplying all the numerators together and all the denominators together.
   For the ratios 2:7, 5:3, and 4:7, the compound ratio is: 
   \((2 \times 5 \times 4):(7 \times 3 \times 7) = 40:147\). 
   Hence, Compound ratio of 2:7, 5:3, and 4:7 matches with III. 40:147.
3. Equivalent Ratio: For any ratio \(a:b\), an equivalent ratio can be formed by multiplying both terms by the same number. 
   For 2:7, multiplying both terms by 2 gives: 
   \(2 \times 2 : 7 \times 2 = 4:14\)
   Thus, Ratio of 2:7 is same as matches with IV. 4:14.
4. Equivalent Ratio for 5:6: An equivalent ratio keeps the same proportion by multiplying both sides by a common factor, such as 5:
   \(5 \times 5 : 6 \times 5 = 25:30\).
   Consequently, Ratio of 5:6 is same as matches with I. 25:30.

Based on these calculations, the correct matches are:

• (A) - (II)
• (B) - (III)
• (C) - (IV)
• (D) - (I)

Thus, the correct answer is:

(A) - (II), (B) - (III), (C) - (IV), (D) - (I)