if A: B = 3:4 and B:C= 7:9, C:D = 2:3 and D is 50% more than E, find the ratio between A and E
(a) 2:3
(b) 3:4
(c) 3:5
(d) 4:5
Answers
Given :- A: B = 3:4 , B:C= 7:9, C:D = 2:3 and D is 50% more than E .
To Find :- A : E = ?
Solution :-
→ A : B = 3 : 4
→ B : C = 7 : 9
→ C : D = 2 : 3
So,
→ A : B : C : D = (3×7×2) : (4×7×2) : (4×9×2) : (4×9×3) { Refer to image . }
→ A : B : C : D = 21 : 28 : 36 : 54
Let A, B, C and D are 21x, 28x, 36x and 54x respectively .
now,
→ D = 50% more than E
→ D = 150% of E
→ D = (150/100) × E
→ D = (3/2) × E
→ E = (2/3) × D
→ E = (2/3) × 54x
→ E = 36x
therefore,
→ A : E = 21x : 36x
→ A : E = 3 × 7 × x : 3 × 12 × x
→ A : E = 7 : 12 (Ans.)
Hence, the ratio between A and E is equal to 7 : 12 .
Shortcut :-
→ D = 50% more than E
→ D = 150% of E
→ D/E = (150/100)
→ D/E = (3/2)
So,
→ (A/B) × (B/C) × (C/D) × (D/E) = (3/4) × (7/9) × (2/3) × (3/2)
→ (A/E) = (7/12)
→ A : E = 7 : 12 (Ans.)
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