If \(A:B=\frac{2}{9}:\frac{1}{6}\), \(B:C=\frac{2}{7}:\frac{5}{21}\) and \(D:C=\frac{7}{10}:\frac{3}{5}\), \(D:E=\frac{5}{7}:\frac{3}{14}\) then
Match the List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| A. | C : A | I. | 32 : 7 |
| B. | D : B | II. | 24 : 7 |
| C. | B : E | III. | 35 : 36 |
| D. | A : E | IV. | 5 : 8 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-IV, B-III, C-II, D-I
The four ratios are first turned into whole numbers and then joined into one continued ratio A : B : C : D : E, by making the common term equal each time. Every pair asked for can then be read off it.
Each ratio in whole numbers (both terms multiplied by the LCM of the denominators):
A : B \(=\frac{2}{9}:\frac{1}{6}=4:3\) (× 18)
B : C \(=\frac{2}{7}:\frac{5}{21}=6:5\) (× 21)
D : C \(=\frac{7}{10}:\frac{3}{5}=7:6\) (× 10)
D : E \(=\frac{5}{7}:\frac{3}{14}=10:3\) (× 14)
Joining them (the common term made equal):
A : B \(=8:6\), so with B : C \(=6:5\), A : B : C \(=8:6:5\)
D : C \(=7:6=\frac{35}{6}:5\); multiplying all by 6, A : B : C : D \(=48:36:30:35\)
D : E \(=10:3=35:10.5\); multiplying all by 2, A : B : C : D : E \(=96:72:60:70:21\)
(A) C : A — this matches (IV) 5 : 8. \(60:96=5:8\), dividing both by 12.
(B) D : B — this matches (III) 35 : 36. \(70:72=35:36\), dividing both by 2.
(C) B : E — this matches (II) 24 : 7. \(72:21=24:7\), dividing both by 3.
(D) A : E — this matches (I) 32 : 7. \(96:21=32:7\), dividing both by 3.