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If $${\text{A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8}{\text{,}}$$ $${\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9}$$ and $${\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4}{\text{,}}$$ then find the ratio of A : B : C : D = ?
Answer & Solution
Correct Answer:
Option
C
$$\eqalign{
& {\text{A}}:{\text{B}} = \frac{1}{2}:\frac{3}{8} \cr
& \Rightarrow {\text{A}}:{\text{B}} = 8:6 \cr
& \Rightarrow {\text{A}}:{\text{B}} = 4:3 \cr
& {\text{B}}:{\text{C}} = \frac{1}{3}:\frac{5}{9} \cr
& \Rightarrow {\text{B}}:{\text{C}} = 9:15 \cr
& \Rightarrow {\text{B}}:{\text{C}} = 3:5 \cr
& {\text{C}}:{\text{D}} = \frac{5}{6}:\frac{3}{4} \cr
& \Rightarrow {\text{C}}:{\text{D}} = 20:18 \cr
& \Rightarrow {\text{C}}:{\text{D}} = 10:9 \cr
& {\text{A}}:{\text{ B }}:{\text{C }}:{\text{D}} \cr
& 4{\text{ }}:{\text{ }}3 \cr
& \,\,\,\,\,\,\,\,\,\,3{\text{ }}:{\text{ }}5 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10{\text{ }}:{\text{ }}9 \cr
& \overline {\underline {{\text{ }}8{\text{ }}:6{\text{ }}:10{\text{ }}:{\text{ }}9{\text{ }}} } \cr} $$
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Login4 : 3
3 : 5
10 : 9
Since C has different no 5 and 10 for determining the
Ratio of A:B:C:D we should equalised the values by
Multiplying the value 2 in
ratio B : C = 2(3 : 5) = 6 : 10
Now the value become
A:B:C:D
4:3
6:10
10:9
now B has different value ie 3 and 6
So to equalised the value we should multiply the value
2 so
in ratio A:B = 2(4:3) =8:6
Now A:B:C:D
8:6
6:10
10:9
So the value become 8:6:10:9
3. : 3: 5: 5 (extend left term 3 to left and right term 5 to right)
10:10:10:9 (extend left term 10 to left)
Multiple as : (4*3*10=120, 3*3*10=90, 3*5*10=150, 3*5*9= 135)
So, 120: 90: 150: 135
8: 6: 10: 9 (after dividing above by 15)
A:B=8:6=4*2:3*2=8:6
B:C=9:15=3*2:5*2=6:10
AB last number is 6 but
BC first number is 6
So CD=10:9
A:B:C:D=
8:6:10:9(ans)